Have your character solve the problem. But the Nagant is a big heavy, hard to conceal weapon. Give her a .22 Berreta or (.22 Deringer), she can put together a makeshift sound suppressor using a half-used toilet paper roll. Have her stuff the roll with a wad of toilet paper, crunch it down with her shoe. She can stuff the little .22 in the roll's tube, push it to the back of his head and he'll drop like a sack of potatoes falling off a truck. It'll be fairly quite. The makeshift suppressor will let you character grow.
Take a look at this on Youtube:
http://www.youtube.com/watch?v=_5oBxytsINM
Good luck,
L