Me, personally, it has to go, first choice is hoping the wife is awake and willing to help deal with the situation with love making or a bit of hand relief but if not it's self masturbation and then if time permits a couple of hours sleep.
Love making definitely first choice. But one odd thing I've found is if I have sex with a wake-up erection I find it difficult to cum - sometimes I don't cum at all. But if I let it go away and make love later with a 'normal' erection it's OK. Anyone else get this?
But I'm also really bad at hangovers, and I spend most of the day groaning, whining, crying or farting, none of which is much of a turn-on for my wife.
My key tactic is to downplay how hungover I am, and practice a bit of seduction first thing in the morning. Then after we've had amazing hungover sex, I can crack on with all the unattractive whining etc. Or eat an enormous full English breakfast - also not very sexy.