After a prolonged period of time, your explorers in .25g are going to have a difference in physiology from their forefathers. A good example of this is shown in "The Expanse".
This will inevitably impact weapon design. High recoil weapons will likely remain in the purvue of specialists. The reasoning is that with less gravity, there is no longer the need for high density bones. That means the skeletal structure of the mass of people would be risking breaking bones or shoulder dislocations with a high power rifle rather just a mild bruise from something larger than a .308 Winchester round. Even Muzzleloaders could have a substantial kick. So lets look at other weapons from the 17th century.
The Longbow might still be in use, but it won't be as strong as the Earth Prime version. The lethality would come more from better arrowheads. The Reasoning is that with the weakening of the skeletal structure, the higher draw weights simply won't be possible.
Crossbows could also work because they rely on mechanical advantage mechanisms to cock like a goat leg lever or a windlass so the strain is not on the skeleton and muscles to maintain draw.
Slender, very sharp personal weapons like foils and rapiers or long slender daggers are going to be likely for most residents of the low G world. They rely on precision and a sharp edge to do damage rather than momentum.
Body Armor is going to change radically. Heavy Plate is just too heavy to carry. Silks and synthetics are going to be focused on. Stuff to stop the cutting edge, so to speak.
Of course on earth we continued to develop chemically powered weapons, mostly in ways to improve loading and rate of fire as well as rifling, but the core of the firearm, a tube that uses an explosion to throw something out of a long tube. On the low gravity earth, you are going to see more experimentation with rockets and bombs. Triggers, Proximity sensors, guidance, and shrapnel. Maybe even rockets as delivery systems for Poisons. I think these will develop faster than Earth Prime, because Firearms are such an effective method for killing.
I'm guessing you will have to account for some things like this