Are you building a hunting rifle or a target rifle?
PRS style shooting or ?
Suppressor? Muzzle brake?
If it's a target or competition rifle I'd stick with steel. If it's a varmint rifle firing long shot strings I'd still go all steel.
If it's hunting rifle you're not planning on firing more than 3-5 shots at a time I'd go carbon wrapped.
On a barrel that short you're not going to see much benefit in weight savings or "stiffness". The carbon wrapped barrels are more for hunting rifles than anything, longer barrel that's still stiff but still light. My Christensen rifle has a carbon wrapped 24 or 26" barrel and it's definitely lighter than dads rem sendero with the same length barrel. I've never stuck them on a scale but you can definitely tell a difference. On the flip side my barrel heats up enough after 5 shots there's a shift in impact and mirage in my scope is terrible. My all steel rifles I can get 10 or so before I really see mirage.
My rifle is for hunting and a dream to pack I'll fire at most 3 shots at a time so I'm not worried about it heating up. I love the look compared to an all steel barrel but it's not anymore accurate than my other rifles in 3 shot groups. It's all in what you plan on doing with it.