NASA has provided a somewhat-intimidating overview of the whole process of proposing, building, certifying and flying CubeSats under their CubeSat Launch Initiative.
There are performance specs for both the CubeSats and their dispenser interfaces on the NASA Resources page. But they don't contain a lot of "don't do this" standards, instead using language like "CubeSats shall comply with NASA guidelines for hazardous materials."
The most fundamental safety standard in this area, the one that i.e. the CubeSat dispenser docs refer to, is called "RANGE SAFETY USER REQUIREMENTS MANUAL VOLUME 3 LAUNCH VEHICLES, PAYLOADS, AND GROUND SUPPORT SYSTEMS REQUIREMENTS" a.k.a "AFSPCMAN 91-710, Volume 3" by the Air Force Space Command. It's a big document, but the relevant parts are probably Chapter 12 "Flight Hardware Pressure Systems and Pressurized Structures", Chapter 13 "Ordnance Systems" and Chapter 18 on rocket motors. They generally don't set specific standards on performance. Rather, they specify that analysis has to be done to ensure that the designed performance is met. For example, Chapter 12 has language like:
220.127.116.11. Airborne hazardous pressure systems shall be designed to be single fault tolerant against inadvertent actuations that could result in a critical hazard during prelaunch operations. Structural failure of tubing, piping, and vessels shall not be considered single failures provided they meet the requirements of this volume.
18.104.22.168. A pressure system shall be dual fault tolerant if the failure of two components could result in a catastrophic hazard.
That approach extends to operations (it's not safe if you don't ensure it's operated safely):
12.1.4. Flight Hardware Pressure System Operations. The requirements for operating hazardous pressure systems found in Volume 6 of this publication shall be taken into consideration in the design and testing of these systems in addition to the general requirements identified in 12.5 of this chapter.
The detailed analysis standards are, well, detailed:
22.214.171.124.1. General Requirements:
126.96.36.199.1.1. A detailed and comprehensive stress analysis of each pressure vessel and pressurized structure shall be conducted under the assumption of no crack-like flaws in the structure
188.8.131.52.1.2. The analysis shall determine stresses resulting from the combined effects of internal pressure, ground or flight loads, and thermal gradients.
184.108.40.206.1.3. Both membrane stresses and bending stresses resulting from internal pressure and external loads shall be calculated to account for the effects of geometrical discontinuities, design configuration, and structural support attachments.
220.127.116.11.1.4. Loads shall be combined by using the appropriate design limit or ultimate safety factors on the individual loads and comparing the results to material allowables.
18.104.22.168.1.5. Safety factors shall be as determined in 12.2.
22.214.171.124.1.6. Safety factors on external (support) loads shall be as assigned to the primary structure supporting the pressurized system.
The basic requirement that these analyses be done and documented is perhaps easiest met by not having pressurized systems, ordnance, and rocket motors on board. The second easiest approach is to use pre-approved units in standard configurations. Trying to roll your own is likely to be very, very hard. Getting XKCD's Safety Sat approved would be an interesting training exercise...