Well, another “dry” option is tumble-dried.
I disagree that it’s a compound verb issue, though. The verb is being modified by the word before it (sun-dried, air-dried, oven-dried, line-dried, freeze-dried), so it only makes sense to change the tense of the verb, not the modifier. The only problem is figuring out which verb in the compound is the modifier. In this case, it’s obviously “blow”, since there the meaning of the sentence is greatly altered by using “blow” alone, but remains the same with “dry” alone:
I blew my hair.
I dried my hair.