There is no "quick sell" option at vendors for this. Instead, you can ask your companion to sell your junk items for you.  Press <kbd>N</kbd> to bring up your crew page, then press the button to sell all junk items (on the right side). 

When you do this, your companion will leave for 60 seconds with the items, then return with credits. You can do this from anywhere, so assuming you don't need your active companion for a fight you can do other stuff while he's gone.  When he returns, he'll be active again (no need to resummon).

Your companion will not sell items above "gray" level.

Source: beta,pre-release and release gameplay