Injured pigeon

Hi everyone, 

I have found a pigeon in the garden who isn't flying (walks/runs away from us if we go near him) and looks a bit weak. We've had two in recent days having a wee battle and flapping their wings against each other so perhaps he was injured then? 

He does seem to be able to spread his wings when he hops up and down things in the garden but he doesn't seem to be attempting to fly. One wing is also drooping down further than the other. 

As it is hot out we've given him water on the ground and he can't fly to the bird bath to drink, as well as some seed. 

However to complicate things, we have two cats (who are being kept inside for now) and several neighbourhood cat visitors so I'm a bit concerned for him remaining on the ground. What is the best thing to do in this situation?

Thanks in advance for any advice!