You should only need a thread adapter and not a whole new barrel.
The barrel should have threads on it that are made for a thread adapter. if you lock the slide back there should be a thread protector on the last half inch or so on the barrel. The gun should also have came with a wrench to be able to take it off or put it back on.
Where are you located? Most of the shops that sell .22 suppressors have the thread adapters.
Huntertown Arms makes some really nice ones that have a hex head built into it so you can use a real wrench instead of the one that Walther provides (its kind of a pain).
If your going with the Sparrow you should want a Silencerco brand thread adaptor because it has the o-ring engagement on it. It will work with other suppressors too, it will just engage the o-ring and keep your threads clean.