Hey there.
To answer your immediate question, no, it's not strange at all to want sex, especially if you've never done it.

The stranger part might be a little unique, but if it makes you feel better, I often wonder about the same thing, though I've no desire to actually "make it happen" (so to speak) right now (I'm waiting for "the one" and all that before I make that commitment

). I don't think I'd be making an unsafe wager if I said you were less interested in the "stranger" part than you are the "wanting to be held" and the newness of it. Am I correct in hazarding that guess?
Anyway, I would tell you that in my experience, I've never heard anyone lamenting they "lost it" too late, but more than a few for too soon. I think you've plenty of time to establish a relationship you feel comfortable in before you do this.

Ultimately though, it is your decision. I'm just speaking from the perspective of what I'd do, is all.
Speaking honestly, I have absolutely no clue how one would go about arranging it, so I can't quite help you with the details there. It's never really occurred to me to think of it as an arrangement...I've always just thought of it as something that sort of happens (either inside or outside a relationship). The only thing I can really think of as an arrangement is something like a personals ad on a website or something, but that, to me, strikes me as a gigantic risk. I'm concerned about the people you'd attract.
I don't quite know if your risk for STD would be "much" higher, but again, I am worried about the types you'll attract if you market yourself as looking solely for a sexual encounter, you know?

At any rate, safe sex should be practiced to the absolute best (ie don't do it if you can't

) of your ability.
I do apologize I couldn't be of more help in the specifics to your question, and I hope I didn't seem like I was trying to impose my views or anything like that. I'm just worried about the potential risks to you, is all.
I wish you my very best.
Harley