Hair removal products are usually in the 20-50W ranges depending on wavelengths, the lightsaber wannabe hand held lasers are usually in the 500-2000 mW ranges and while those can burn skin and pop balloons they aren't powerful enough to burn hair.

I just don't see them having the technology to make this work, if they had it would have military applications way before shaving ones.

Just for size comparison this is a laser used for soft tissue removal https://upload.wikimedia.org/wikipedia/commons/c/c7/Sharplan...

And even it won't burn hair because it works on tissue with high water content only.