Sending a thank you letter to a research professor?

Is it too late or "awkward" to send him a handwritten thank you note now that it's been about two months since I've last contacted him?

Nope.

Two months is not so long in the academic sense at all. Whether or not it's handwritten shouldn't matter as much, either. Typing it up is perfectly acceptable, readable, and much easier to correct if you make an error.

In addition to Compass' excellent response, I'll suggest a few other things you can do:

• Make a small donation to the college in honor of the professor. He will be notified.
• Cc the letter about how helpful he was to his department head and/or Provost.

FWIW, I'm a professor and save all such letters and emails.

The timing would be even better if you wrote him upon getting accepted into a graduate program - then you would also be informing him on the news. Of course, @espertus' suggestion are quite relevant (and no less relevant when you get accepted somewhere).