Unfortunately there is no quantifiable or simple rule here, as his threshold for embarrassment will vary in proportion to his shyness and his pride, which are different in every man. Well, for starters, in the early stages, you will need to give him blatant signs of your interest.
Aside from their innate male tendency to overlook anything that isn't spelled out in black and white, shy men will by default doubt any sign of your affection.
This is what prevents them from taking the initiative in the first place.
Though he knows his own limitations (as prescribed by his shyness), he also knows what a typical man is "supposed to do." So he recognizes, too, when you are doing it for him.
This will offend him if you flaunt it, or if it is evident due simply to the social magnitude of the task you've assumed (for example, if you take his hand and lead him through a crowd).
If you are looking for an abundance of devotion, he has it to give.
So, in conclusion, if you are interested in a shy man, start by questioning that feeling.