So set a reasonable donation request. The huge percentage of those wanting to adopt a cat will pay it, and you can absorb the very rare person who can afford to properly care for a pet but can't afford the "purchase price".
Look at it this way: many of those who won't or can't buy a pet are those who don't properly take care of them and/or who dump them when they become too much of a hassle or burden.
So you're actually being compassionate by setting a fee or suggested donation.
I bet you could steer your feelings in that direction if you worked at it a bit.