Yes you could use cat contracts. You could work with your local shelter.
If you are taking care of strays and adopting them out by yourself as a gesture of goodwill, be careful. You are assuming some liabilities on yourself depending on where you live, you could get into legal trouble.
The things to avoid.
Giving your strays "free to good home"
only give the stray to someone you do know or knows someone who you know. (this is hard i know) or if this is not possible.
Dont let the pet go with people that your "inner self" gives you warnings about.
If your conscience nags you about something someone said during your talks. Dont pass it off, especially if it is a stranger. Talk to people. the more the talk the more the let you know about what kind of person they are. If you refuse to give the animal to someone, they may get upset. DO NOT take this personally or be offeneded. You are looking after an animal that cannot speak for itself and you are making a judgement call in its best interest.
Never give out a stray to groups of teen-age boys or groups of young men. especially groups of middleclass white men. (I am only stating risk groups keep the PC crap away)
I am always happy when a cat i have seen longing for a home, get a good home.
But i always wonder if they are ok. Its tough to let go of that cat you cared for. they touch your soul. Given the resources i would have hundreds of cats on a ranch in utah or montana somewhere so i wouldnt feel the same way you did. But thats not going to happen, so i take the risk of trusting someone to care for the cat as much as i would.
THANK you for taking care of strays and helping the find homes!!!