Over the years I've managed aptasia via peppermint shrimp, CBB, filefish and kalk paste. Each of these methods have worked well for me.
Peppermints = hit or miss whether they will eat aptasia, but if you get several shrimp they'll likely resolve the problem. I've never seen my peppermints damage any other coral and find them a useful member of my tanks maintenance crew.
CBB = supposedly hit or miss - mine have always had an appetite for aptasia, though they also like the small feather dusters that come in on LR. Can supposedly be difficult to feed after the aptasia and feather dusters are gone, but I've had no problem feeding them my standard frozen fare. Requires a larger tank as an adult.
Filefish = I used one about 20 years ago and it devoured the aptasia. The species I used IIRC was a Chaetodermis penicilligerus (tassleated filefish). I found him to be a model citizen and didn't bother my other corals, but requires a large tank.
Kalk paste = easy to mix up, inexpensive and works. You fill a syringe with kalk paste, squirt it into the mouth of the aptasia, and boom, it's dead. A good method if you have a small infestation, but obviously only works for the aptasia you can see.
If you buy corals, you will almost inevitably get aptasia from time to time. You can minimize the chances by looking at coral plugs during your dip. Learning to deal with aptasia is just part of the reefer learning curve.
I currently employ three or four peppermint shrimp in each of my tanks and they do a good job of removing the aptasia and are generally useful and interesting to watch.
To the OP, since you're already considering a massive LR change, I'd recommend instead that you pull the wrasse temporarily and go with 3 or 4 peppermint shrimp to clear your problem. Alternatively, look to a CBB or Filefish if they're available and you have room (or can rehome them after the problem is sorted).
Good luck.