So if I am correct there are several ways I would try ... ;)
1.) Think of a really hot girl which would fuck you and try to get a hard on. This would work fine, if you try really hard, maybe a orgasm is possible? I guess not ...
2.) Rub your dick between your legs. I think this will be very hard to cum but possible I guess
3.) Just do some gym bend over train your back and hope that your cock is big enough to suck it, no hands are needed this would be a sexual perpetuum mobile
4.) Do it my way ;) just kidding but it is an option:
Only thing I am not allowed to use are my hands, ... So wait until 12:00. Look at your wife and ask her why lunch isn't ready and bring her to be really really sorry. Than stand up look at her and tell her to get immediately on her knees. It is time to suck for forgiveness
I guess this would be my favorite to get an orgasm followed by all the other ways by using just two or three words

english is not my mother tongue, so please tell me my mistakes and don't feel offended ;)