HARP fired projectiles from a gun into suborbital trajectories. This type of projectile carried a scientific payload, but did not have any reaction engines (although later proposals did). Their designs evolved over the years, but it seems like the general shape of the projectile was always in a genetic rocket shape, similar to this:
How does a rocket shape make any sense, considering that this didn't have engines? The drag coefficient of this shape looks to be about 0.75. On the other hand, alternative shapes have lower coefficients:
If we were to superficially accept these numbers, HARP could have achieved a significant reduction in atmospheric losses by switching to a droplet shape, possibly by a full order of magnitude.
The fins obviously have some role, but I don't see how they impact this discussion. If you have a tapered end, that could still have fins. Stability of its orientation is obviously important - does that restrict the shape? Or, does the modeling of drag coefficient fundamentally change at several mach numbers, so that there would be no benefit to the tapered end? To my knowledge, all projectiles had a disposable portion that held it in place as it moved through the barrel, so it seems like that would make any shape practically workable.