IMO, saying "I do not communicate that way, sorry" on an initial contact request is a little douchebaggy (key sentence is "on an initial contact").

I much rather prefer: "I'll make time for a quick phone call, but I only have X minutes for it." (5 minutes? Does not have to be a long time). Stick with the time limit.

The first thing to say in the phone call is "This may be the last phone call we have because [...]". That's better than coming off as some eccentric whose most memorable quality is that he does not do phone calls. As opposed to whatever you want the most-remembered thing about you is.

Just an opinion.