Can I just cap the red wire from a dual switch to install a ceiling fan without a light?
Nope, can't do it.  

Code absolutely requires a wall switch in the room that works.  

There's a variance that lets you have that wall switch operate a receptacle, and then you're supposed to plug in a floor lamp and leave it switched on 24x7 at the lamp (or just remove the switch knob; that's what I do).  However no, you can't have only lights which must be operated at the lamp, with a phone, what have you.  

You'll either need a different fan, a light kit for this fan, a ceiling light elsewhere in the room, or the switch must operate a receptacle.  (there aren't Code police who go around checking to see if you actually plug a lamp into it lol.  But you will certainly have problems when you sell the house; it'll get redflagged and you'll have to fix it, right in the middle of the hustle and bustle of the property sale).