The second image is nonsense, most likely someone not familiar with what they were putting together for the display.
My question is, which one is actual representation of the docking orientation?
First one is correct, latter is rubbish.
and is skewed orientation really better?
skewed prevents the docking system from working.
Before the current Kurs (Course) system used for docking the Russian spacecraft today, there was a system called Igla (Needle), introduced 1965-67.
Look at this:
and compare it with this:
Comprised of matching radar equipment on both spacecraft, Igla provided data that was used for controlling both the relative motion and the attitude of the two approaching craft.
The passive craft was equipped with a radio system that could provide a radio beacon for homing by the active craft or a transponder function for measuring range and range rate.
An important note was that Igla depended on LOS, line of sight, so if one craft were to roll or change attitude, the other would end up chasing it to regain LOS and re-engage. (Kurs improved upon this and no longer requires chasing, wasting valuable fuel).
As you can see from the image above, Igla relies on matching pairs of transmit and receive equipment.
spacecraft 2 transmits a beacon signal through its transmit antennas (mounted front and back)
rotating search reception antennas (mounted front and back) on spacecraft 1 pick up the beacon signal.
reception antennas on spacecraft 1 are used to point the longitudinal axis of 1 at spacecraft 2.
once aligned, spacecraft 1 transmits signal through its narrow beam antenna dish (tall, unfolded, at front) at spacecraft 2.
spacecraft 2 picks up the narrow beam antenna signal using all of its transmit/reception antenna (front and back). This is used to align spacecraft 2's narrow beam antenna dish (tall, unfolded, at front) so it points at spacecraft 1.
Both spacecraft aligned, the beacon signal is turned off. As both spacecraft approach, the signals between the narrow beam antenna are used, a secondary antenna is used to counter parallax errors.
Igla was developed because it was anticipated early in Soyuz development that it would be used as an unmanned tanker for future operations (something it fulfilled much later with the introduction of enormously successful Progress unmanned cargo-tanker spacecraft in 1978).
Igla when attached to both Soyuz and a Salyut space station:
So, in summary they had to line up and not be skewed because the docking system dictated that they have direct line of sight to be able to communicate and determine roll and attitude in relation to each other.
Here is a video (on the right) from Soviet TV of the EVA after Soyuz 4 and 5 had docked.
Sven Grahn has an excellent resource here:
and he has the NASA translation of Kratkoye opisaniye radioapparatury sblisheniya kosmicheskikh korabley tipa Soyuz here:
It is worth noting that Kurs (Course) replaced Igla in 1986. Kurs is fully autonomous but has a manual backup called TORU, introduced in 1993.
Up until around 2012 Kurs still used around 5 antennae.
The recent version replaced five rendezvous antennas with just one (whilst retaining two older antennae):
As you can see, they still need to line up.
The only time that Soyuz had docked without lining up the antennae is when they had to dock with a, at the time, dead Salyut 7 space station in 1985. The station had no operable beacon (complete power loss) or attitude control so Soyuz had to be flown manually, chasing and matching the rotating stations docking port. Range was carried out with a handheld optical rangefinder.
However, one would have to guess that they still probably tried to line up (there is no information or pictures to say either way) as normal because of the docking collar latches.
Once the probe has been accepted in the drogue, a motor screws them together and then latches lock on for the hard docking. If the latches are not over those corresponding receptacles then they are not going to latch.
Importantly, the Soyuz/Progress/SSVP docking collar, from Soyuz 10 onwards (no internal transfer prior to this), has various holes and nozzles at particular places that allow fluid, gas, and electrical connections. If you dock skewed then you are not going to get those connections.
Couple of links for the Kurs-NA (Course-New Active):
Kurs-NA will use less power than the current Kurs-A system, and also will replace five existing rendezvous antennas with just one, thus saving mass on launch.
...replaces the function of five existing Kurs-A antennas into one antenna, thus allowing for the removal of four antennas from future Progress and Soyuz spacecraft.
(says 1 replaced 4)
https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=2020-050A and https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=2018-058A and https://space.skyrocket.de/doc_sdat/progress-ms.htm
states same as russianspaceweb.
Quite a bit more than usual about Kurs-NA in 2016:
Reaching the 200-Kilometer communications zone around ISS, Soyuz powered up its KURS-NA System that had completed flight testing on four Progress missions before being introduced on the Soyuz. The new system reduces the amount of antennas installed on Soyuz, cuts the mass of the system and delivers better accuracy.
Once activated, KURS-NA searched for beacon signals coming from its KURS-P counterpart on ISS to lock onto the Station’s signal and re-orient Soyuz to face the new AO-753A phased array antenna toward ISS for pitch and line-of-sight angle measurements.
AO-753A, installed on the Orbital Module, replaces the VKA omni-directional antennas used in the early rendezvous phase and the complex 2AO rotating antenna that was previously used for angle measurements during the far-field rendezvous. Later in the rendezvous, KURS used the two ASF-1 antennas retained from the KURS-A system to deliver range and range rate information in addition to the angular information.
A two-way communications link between Soyuz and ISS was established to enable the crew to talk to Mission Control Moscow as they continued watching over their spacecraft. The 34.27m/s DV5 burn at 3:00 UTC delivered Soyuz to a trajectory towards is Ballistic Targeting Point, offset one Kilometer from ISS to preserve the option of a passive abort until late in the rendezvous when the targeting offset was reduced.
Soyuz continued under automated control after the KURS-P on ISS and the KURS-NA on Soyuz was checked twice, at 45 and 15 Kilometers. Starting the close rendezvous, Soyuz conducted a series of impulse maneuvers, swinging back and forth between line-of-sight attitude and burn orientation.