Well maybe, but it has to be a completely new unit, as you say, That means it must be made by a specialist double-glazed unit manufacturer.
Make sure that your glazier specifies the correct unit thickness - building regulations require a bigger gas gap than previously, and your door may not have a rebate that's deep enough. In that case your glazier must specify a narrower unit. The new glass must be toughened, and the inner leaf should be Low E glass to comply with current requlations.
Your glazier will know that it's not possible to cut toughened glass - the glass must have the cut-out for the cat flap made in both pieces of glass before they go to be toughened. The double glazing manufacturers will handle all that.
If you want the best cat-flap around, go for a Staywell 500 infra-red. It has specially coded collar keys, so only your cat(s) can get in. if your budget doesn't like a £50 + price tag get the Staywell 400 magnetic collar key flap at under £30