One of the 'Doctor Who' groups I belong to on Facebook is "The High Council Of Time Lords". A couple of weeks ago they posted this picture:
I suppose they could have been channeling Ash from the "Evil Dead" movies for this mash-up, but we're telecentric so the biggest options would be either Sam Axe of 'Burn Notice' or the title character from 'The Adventures Of Brisco County, Jr.'.
I'm going with Brisco, if only because his Western TV series was already geared for science fiction. Brisco County, Jr. might have rustled up a ride with the Doctor to the early part of the 56th Century to track down the orbs and prevent a new threat to the dawn of the 20th Century.
If they did share an adventure in the TARDIS, at one point Brisco must have needed a change in wardrobe. And according to this picture, he would have helped himself to the Fifth Incarnation's cricketer outfits.
But overall, I think Brisco might have felt more at home either in the garb of the Doctor's Fourth Incarnation - just for the loose fit and the length. Or maybe even something simpler, like the jumper worn by the Ninth Incarnation.