What's the best way to relocate my wall vent?
Yes, you can shorten the duct as needed. If you need a crimped end to fit the new boot, a needle-nose pliers from the end and a bit of twist will create that for you.
If you're not running full ducting*, you'll need to either relocate the outlet or box around it with lumber so that it's not technically in the same cavity as the duct flow. Use silicone or some other fire-resistant caulk to seal the holes in the studs.

* Modern code may require full fire-resistant ducting for supply vents.