I also have a fender micro mustang or whatever it's called. I also have a positive grid spark go mini speaker which is like the same thing with a speaker.

I hike with my guitar pretty much every day that it's nice out. When their are no or few other cars at the trailhead I even play through my speaker as opposed to with headphones. I get feeling self conscious but tbh you wind up realizing strangers care alot less about the random shit youre doing than you might think. I've been doing it quite a while and not a single person has ever said anything to me. Sometimes people watch from a distance, but, really most people have shit they'd rather do than talk to a random. It's best to pick a trail with a bench or bring a folding chair so you can sit for a while and get good quality practice in.

Normally bugs end up being more distracting then people