I do not recommend recaps. You've seen the chunks of rubber along the freeway. If an 18-wheeler blows a tire, it has 17 more. If you blow one, you have 3. Big difference and not worth the increased chance of an accident. 

I didn't think anyone was retreading passenger car tires these days. A potential problem might be that tires last so much longer than they did back when retreads were popular 50-60 years ago. You could wind up with recapped tires that have new treads installed on carcasses so old that they won't last long before the sidewalls start rotting out.

Retreading modern tires are uncommon but yes. If it's done on a modern tire then it can be just as safe as a regular tire. I would suggest hot, as it uses the same process as factory made new tires.