Trapping? stray kitten 6-7 weeks old

Hello my husband found a stray kitten in our driveway a few nights ago. It looks to only be 6 or 7 weeks old. Very tiny, but also very fast. We have been feeding it wet cat food and some milk replacement. He/she comes at various times in the day, but can’t predict when he will show up.

We have discussed trapping him, but aren’t sure how or where to take it once we have. Any suggestions? Maybe a kitten rescue center? We don’t want to contact animal control as we have heard they sometimes will euthanize them. We also can’t keep the kitten because we have two large dogs.