Kiss
Keep it simple, sister.
Gun shy usually also means not interested in becoming proficient with guns, moving up in caliber and complexity, etc. Such people still may want a gun, but it has to be the simplest, easiest and most effective one possible--requiring the least training. My daughter used to fit that profile. When she had a baby, she decided to get a gun.
I showed her one at a gun store. We bought it. She still has it and would use it first although there are numerous other guns in their home now.
It is a simple side-by-side 20 gauge coach gun (short barrels) with five extra rounds in a sleeve on the stock. Two triggers. Easy to load and shoot, from the hip. #4 buck. She practiced with #8 bird shot for $3.99/25 from WalMart.
When you look down those two tubes from the wrong end, they might as well be howitzers. The initimidation factor is huge. No complex loading/unloading, pumping, etc. Slide the safety, bang bang.
Not for everyone of course, but this might fill the bill in this instance.
CB3