+1 for either some kind of tranquilizers and taking her to the vet, or trying to get a vet to make a home visit.
It's not that there's anything morally wrong with the gun method, it's just that I can't help feeling that's not how you want to see her go.
Are there any sleeping pills in the house? Might be worth trying a few of those to get her off to sleep before taking her to the vet.
Good luck with whichever way you decide, and my sincere condolences.