From being many years as a male, I can tell you, morning can be fun or miserable depending on your partner and what you make of it. Worst is having to pee real bad but you can't. The upstanding issue had to be alleviated first. I have been known, many times, to take things into my own hands to get the darn thing out of the way. Go with the intensity of your problem, it will guide you (sometimes falsely so deal with that as well :/).
Age and medications (not HRT) have surely already shifted my levels down. No more many-times-daily arousals and morning 'wood' is now morning 'noodle'. I do not miss being governed by an appendage that has no thoughts behind it .. however enjoyable it was at times. I feel so much more normal and myself now. But that wasn't your question.
I'm not sure I helped in any way but you're welcome to ask. PM if it feels to explicit, I'll answer the best that I can.