Yea i think you should
Explanation:
Frankly, the best way to do it is to just be chill about it. Just be like; "hey bro happy late birthday!" and then if he starts a convo with you just keep it casual, or you can ask stuff like; what did you do for your bday yesterday? or like how you been? or whats your next class? etc.
Basically, be aware that he likes you, but unless you like him back, don't change the way you interact with him.
Do not get all awkward and be like; "he so i know we haven't talked in a while but i know your bday is today, sooo umm happy birthday" and run off.
If you want to continue interaction with him in the future, since he's apparently shy, it may be up to you in the near future to initiate conversation with him until he feels comfortable striking up convo wit you first. ;)