Fledgling Bluetit feeding frequency

Today our cat caught 2 blue tit fledglings in one bite and we got him to let them go. We couldn’t see their parents however and one had a bad leg and the other was lying down. Sadly this one died soon afterwards. We have 4 cats and if we’d left him there we are pretty sure (past experience) he would be caught. I know you should leave them unless last resort but we couldn’t think of how to safely leave him. He has survived overnight so far but seems to have an injured leg- my sister has contacted a vet friend about treating this. Our guess is that they were fledglings possibly just out the nest. We have been feeding it waxworms and mealworms chopped up and dipped in water every 1 1/2 hrs. Should this be more frequent, and if I wake up at 5:30 is this necessary or too late?