Solo mode isn't offline.

Few will frown on you, as you're not affecting anyone if you do. (More people will frown on actively doing power play in solo)

As an alternative, you could build your ship to be a bit sturdier, so you can live long enough to escape to another system.

But last time I did that, in my extremely shielded trading cutter, I kept getting pulled by the same person, even after I demonstrated I easily got away and they couldn't dent my shields. So you still might not get anything done.