I know it will cost, but I'd lean towards adding a younger two way RHD through trade. No one high profile, but solid, that if not already there, could grow into the #4 role quickly.
Is Bear that? If so make space and give him a shot, if not, meh. Who knows though, maybe he takes a 1yr smaller deal coming off an injury like that.
Obviously no better team to prove yourself on.
Who did you have in mind?
Teams generally don't want to make young two-way RHD's available so it seems a bit optimistic to expect to get a potential top 4 RHD for reasonably cheap.
Columbus having a logjam at RHD means Peeke and/or Boqvist are options, but neither are ideal for different reasons. Peeke has a $2.75m X 3 year contract which could be tricky to fit in long-term, but at least there's clarity with Toews so that may be workable still. Boqvist is a smallish offensive RHD who wouldn't fill a need really.
Nashville may decide to move on from Fabbro so he could be a nice option if they'd move him within the division. He's an RFA this off-season with a $2.5m QO so there's some flexibility there this off-season.
Kovacevic fits your description well, as a young and cheap guy who has potential to play up to a #4 role, but Montreal would probably be loathe to move him barring an overpayment.
New Jersey potentially have an excess of RHD's too, and if Nemec and/or Hughes take top 6 roles then perhaps Colin Miller may be made available. His $1.85m x1 deal would be manageable and he only cost NJ a 5th rounder to acquire so likely wouldn't cost much in another trade, though he's more of an offensive type rather than someone you'd want anchoring your PK so that might not be the ideal route.
I also suggested Matt Benning who's a solid if unspectacular 3rd pairing RHD on a $1.25m X3 year contract.
Realistically the Avs will probably just wait until the TDL to acquire a rental RHD so they can assess the market and how guys are playing nearer the playoffs.