I was raised by a step-father, for whom I cared very much and who cared very much for me, as you say your husband and daughters do for each other. It was not unusual for my step-father (who I actually consider my dad) to hug and kiss me like any father hugs and kisses their daughter. I'm sure sometime (more than once), he probably even swatted me on the butt for whatever reason and one time he even had his hands under my arms because I'd sprained my ankle and he had to help me walk. In addition, we lived on a farm and we worked together a lot... there was nothing sexual about any of our physical contact.
I understand that your daughter(s) had the situation with the older male cousin who tried to molest them. I agree with AnnieBrooke that it might be beneficial to see a counselor to help work this out. It will, not only, clear the air between you and your husband, but can help our daughters deal with the situation that happened when they were younger and help all of you get past that.
It's especially important for your daughters to get past it, so they don't spend their lives projecting their feelings toward that older cousin onto every man they meet and expect them all to behave in the same manner. Not all men behave that way (most don't) and I'm sure you want them, to someday, be able to have healthy relationships with men. Counseling does wonders.
All of that said, forgiveness is for the one doing the forgiving in order to be able to move forward.
I always see women being extra careful around men when they have female children. I mean it is understandable, but if you put him under the microscope and try to find even the smallest thing that looks wrong in your eyes - you will find it.
If this guy was a molester I think he would've tried something thus far, and something drastic. Slap on the butt while saying "Good job" is pretty much what we see members of a sport team do it and I guess that was his intent. That thing with arms under her armpits... I really don't get, but it seems you trained both of your daughters do react immediately if there is any kind of physical contact that's going on. Not every physical contact is sexually charged, I hope you understand that. And it seems to me you are seeing this or that cause you want to. So no matter what he does it can seem wrong to you if it involves your daughters in any way.
My advice is: leave this guy. Not because I think he is a possible child molester but because you are micromanaging his and behaviour of your daughters to that point where you will just create a crater between them and him, and it will just cause awkwardness in your household. Do you want him to not have any physical contact with your kids whatsoever? Cause if you saw tickling as act of sexual advances than you can see it everywhere. And if you find stuff like this awkward than maybe the problem is in you. Are you jealous of your daughters or anything of that extent? Do you feel sexually threatened by their presence and youth? Think deeply and be honest with yourself. And stop seeing wrongs everywhere, it is simply not healthy.
It kind of sounds like you are all on edge about this guy and his intentions towards his daughters and stepdaughters. Why is that, has he behaved inappropriately towards them or towards girls in the past? Or have you or your daughters been mistreated in this way by someone else in the past? What's the source of the heightened sensitivity in your family about possible sexual misbehavior? If it is his own past behavior, that seems a valid thing to worry about, but if he is being judged because of something someone else did to you or the girls that was wrong, that seems maybe a little unfair. Did he do something to someone else in the past?