Compact HF/shortwave radios with transmit capability exist, but they're pretty expensive and are generally definitely portable but not quite handheld. The biggest user of such equipment is the military, so a lot of the tech is engineered for that with civilian/amateur use as an afterthought. ICOM, Yaesu, and Xiegu are probably the best known makers, and you're looking at ~$1000 as table stakes for a modern one, though there are some slightly cheaper options.

Handheld CB radios do exist and are cheap, but I've never really used them.