I never feel awkward about my arms.
I have been developing them for 20 years.
My shoulders, biceps, and triceps are all well developed:
I make sure to wear short sleeves as much as possible, and when I wear business shirts, I roll the sleeves up, like a politician ready to get his hands dirty...
I read somewhere that well developed forearms on men read by others to be a subliminal sign of strength. So when I'm in a meeting, I make sure mine are seen, and I usually don't have any problems.