If a girl knows that she embarrassed a boy in-front of someone else (and hurt his feelings), and now it’s uncomfortable for her and maybe inappropriate to call him and ask for forgiveness, and to ask a male relative to call up would be very inconvenient, is it enough if she just davens that Hashem put in his heart to forget about the whole thing?
The halacha is that we have to ask mechila to those that we offended, and it is uncomfortable to do. In truth this is part of the kapara for the aveiro. It is brought that when klal yisroel asks mechila from each other, the satan tells H-shem, “I can’t be mekatreg on Klal Yisroel, they are like angels, they dress in white like angels… and there is peace between them like angels”. In your case if you feel it is inappropriate to ask him, (although you can ask it without getting all friendly, in a businesslike manner, and it shouldn’t be a problem) you can ask someone else. It can also be woman that knows him, to make the phone call for you. The ideas of davening is very b’dieved, only when all else fails.
A gmar chasima Tova, and in the zechus of being mekayem this not-so-easy halacha, H-shem shoud send you a year full of bracha and everything that you need.