I agree, only offer one at a time. You'll overwhelm her or scare her, and she won't eat.
If she refuses them both after a suitable period of time, the fastest way to deal with them, IF they are not big enough to eat and drink on their own, is to lay them on a table, firmly place a pencil just behind their head, grasp the tail, and push down with the pencil while giving a sharp tug on the tail. This dislocates the spine, and they die almost instantly.
IF they are big enough to eat and drink on their own, just get a small plastic critter keeper and save them until next feeding day.
Gale