I'm sorry but you're comparing a Handi in 10Ga to these folks possibly getting one that shoots a handgun round up to perhaps .44Mag? There is simply NO basis for comparing the two. One will try to bust the shooter's collarbone while the other will be stout enough to make the shooter smile the first few times and to not even be noticed when shooting at an actual game animal.
Cdhunter, if you can find a Handi Rifle in .44Mag or a Rossi Winchester 92 clone in .44Mag you would have a great deer gun for the ladies to shoot that would be a great option out to as much as 100 yards or so. And if you fit the rifle with a Limbsaver or similar recoil pad none but the most recoil sensitive would in any way flinch at shooting such a setup.
For folks that do not shoot often a single shot break open has a manual of arms that is easy for most anyone to fathom. It doesn't take much to break, load, close then walk around stalking the game and to #### the hammer and fire. I can't imagine a system that is as inherently as safe.
A close second is the lever rifle. As long as they practice lowering the hammer to the safe "half ####" position or using the safety if there is one that's the only real trick to that style.
And Rossi DOES make 16 inch carbine barrelled options that are not only light to carry but short and handy in dense brush conditions.
And let's not forget the moderate recoil .30-30 cartridge from a lever Winchester 94 or Marlin 336. A classic deer cartridge shot from some VERY classic guns. And one that managed to fill freezers or cold rooms literally from the first year it was introduced. Again the rifles that shoot this round are not overly bulky or heavy. And the .30-30 is the sort of rifle round that would be fine for all but the most recoil sensitive folks out there.