We're experimenting as a Brass-Brass-Bass combo, and wondering what we can do to make the bass's job more interesting (besides throwing in more solos). Is it fairly easy to replace substantial portions with improvised walking-bass style lines and still retain the percussive properties of the bass sound?
A bass player can easily be the timekeeper for a jazz combo without drums.
I'm a bit confused by your question, specifically--
The properties of the timbre are going to be up to your bassist, but on what I am assuming is an electric bass guitar, you should be able to find a representative jazz bass tone: a bit of midrange and not too bright of an attack.
Timekeeping is inherent in a walking bass line, simply because it plays four quarters to the bar. Also, I really can't fathom what the bass player might have been doing instead of a walking bass line. Root movement half notes? Whole notes? Based on what you've stated in the question, I would certainly use a walking bass line as the default setting.
Maybe throwing in a few unison band lines might spice things up a bit?