There are some reasonable-looking ballpoints at Cult Pens, Write Here and The Writing Desk. Names include Faber and Lamy (who offer wooden pens), plus, as noted, some really expensive resin articles from Montblanc and other top-end makers. The prices of some of these are equal to, or more than I would expect to pay for a Scribo or Santini fountain pen with a 14k or 18k gold nib.
There are also several small "artisan" makers, like The Wood Hut, who will produce pens to order. Some of these also make wooden brush handles.
I don't think you'll have too much trouble finding a wooden pen, but as far as I can make out, what you get will largely depend on your budget.
The only wooden pens I own are those penholders for calligraphy nibs, which don't get a lot of hard use and aren't carried around in my pocket. If wooden pencils etc. are anything to go by, I would suppose that any wooden ballpoint that's going to get a lot of use needs to be strongly and substantially built, to avoid breakages, and the Lamy 2000 yew or blackwood models look good for that. I have a 2000 fountain pen, and the shape is just right.