Obviously not as simple as just changing chainset... new front mech, maybe bb, probably rear mech and cassette, possibly even levers... just about a whole new groupset really
Assuming all your components are currently ship-shaped, imho chance is there is very little "collateral damage" to your wallet required.
The main problem is to know what you have, since Veloce has been through numerous generations over the years with different specs.
However assuming your groupset is current, then officially the triple uses a 115mm bb while doubles have 111mm bb (unless bike has oversized tubes then it would also be 115mm). Anyhow since the 115mm is roughly 4mm longer on the drive side, putting a compact on will mean it sticking out same over designed. However because the compact is narrower by nearly the same and because all mechs have leeway to go over, mech reach "should not" be a problem despite committing the sin of reusing the old bb.
Since the existing rear mech obviously can wrap far more chain than the compact yields you can even be lazy (you can call it retaining flexibility for potential future changes) and not even shortening the chain if you don't want to.
The only remaining issue then is whether a triple mech will shift a compact up as well as a double mech. The physics is not very different - a double mech can be seen to have a slight advantage, but all front shifts are agricultural at best (for cure see 1xN below) and it should work if properly adjusted.
Benefit? You will lose around 100g for around £100 unless you beg, borrow, steal or fleabay - I only said limited "collateral damage". £100 for 100g + busy left hand suck, imho.
Actually one move that seemingly and surprisingly hasn't been mentioned much here but is all the rage (even) offroad is going 1xN where N is the number of speeds at the back. Since these days 11-34T and even 11-36T cassettes* are available and many have modern long cage rear mechs already, getting a light single (say around 38T e.g.) chainset, ditching the front mech, associated cabling as well as the front shifter (particularly for flat bars) should probably be considered by more roadies (and softcore offroaders), and they shouldn't even need a chain keeper.
It could be a very liberating experience.
* alas, the fly in the ointment, is Compaq freehub owners need not apply - Compaq cassettes are only available up to 29T