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).
Once this happens, you will need to gradually assume a less assertive (more traditionally female) role, because he will then be more liable to get bored with you, wonder if he could do better, consider his other options (the perception of which his newly-found confidence will likely inflate), fool around, etc.
The second caveat is that even a shy man has pride.
While dating is part of life it should, like marriage, not be your only social outlet.
Even marriages require that the spouses keep their outside friendships to prevent the spouses becoming stale and narrow, and while friendships must never disempower a marriage, dating should not disempower friendships.
The reason for this is that shy men are more concerned with avoiding the social catastrophe of asking you out and failing than they are of getting you.
This is what prevents them from taking the initiative in the first place.
I've dated countless women and it has always amazed me how little they know about men.
If nothing else, this blog is an outlet for voicing my astonishment at the typical female's ignorance of the male mindset.
At most, it is a reliable source of advice for women who want to improve their chances with the opposite sex.