Yes, anyone's partner could be cheating. And if they come on here asking if it sounds like they might be then they could expect equally honest responses! I wish I knew about MN when I was going through similar stuff! It's perfectly natural to feel defensive of your relationship if you feel it's being attacked because its something precious to you, but it really isn't being in the way you are perceiving - your title is "think my OH is cheating...", so no-one is coming up with anything you haven't suggested yourself!
The cookies cannot give you the information you want, but if you're intent on figuring out if the site usage is current or not, how about deleting the cookies yourself and keeping an eye to see if they reappear?
OR... as you've been messed around before and have understandably admitted to finding it hard to trust, you could use that as an inroad to having a conversation with your partner instead. Something like "you know how hard I find it to trust because of xyz? Well I saw this on your computer and it naturally stirred up panicky feelings for me. I'm sure it's innocent and only there from way back, but can we talk about it please to put my mind at rest"? If he's innocent he would have no reason to feel defensive about that, and would be nothing but supportive.
If you're so scared that talking to him will just give him an opportunity to lie, then in the kindest and gentlest way possible, that just isn't proper trust. Maybe it's a hangover from past abuse, maybe he just isn't trustworthy. Either way, feeling anxious about cookies on his laptop and not feeling able to approach him about it is not something you should have to just put up with.
I hope you sort it out in a way you're happy with 