The pasuk says (Devarim 25:18):
תמחה את זכר עמלק- wipe the memory of Amalek.
Does this mean to wipe all of their memories, or only enough to make them ‘non- Amaleki’?

Also, how do we wipe their memories-hypnosis seems pretty close to the prohibition of magic, so are there alternatives?

This question is Purim Torah and is not intended to be taken completely seriously. See the Purim Torah policy.

You only need to wipe their local memory storage. Memory in the Cloud need not be wiped, as the verse ends

מתחת השמים

The best approach is really just to overwrite all of the memory with binary zeros, as the Spies themselves recommended (Bamidbar 13:29-30):

אפס כי עז העם היושב בארץ... עמלק יושב בארץ

Zero out the nation that lives in the Land ... Amalek lives in the Land

I've always interpreted that pasuk to mean the wiping out of the memories of Jews(and Noahites) of any memory of Amalek.

As is usual in a lot of cases, I learned this by watching lots of Star Trek.

Starting with the original series' first season's "Dagger of the Mind" - not so coincidentally written by a 1930's Germany-fleeing Shimon Wincelberg writing under the pen name S. Bar-David - there is memory erasing "neural neutralizer" as a central plot point. Evidently, when they started using it for other things besides wiping out the memory of Amalek, that's when the trouble started. But all turned out well for the mitzvah-observing characters in the end.

Later on, in the Next Generation/DeepSpace Nine's times, Dr Bashir used a memory eraser in the episode "Sons of Mogh" to wipe out the memory of Amalek(and a bunch of other stuff) from Worf's brother's mind for a successful conclusion to the episode.

Btw, it's obvious that Worf was raised in a Jewish household - in the Next Generation episode "Family", his adoptive parents were obviously Jewish, even being played by Theodore Bikel and Georgia Brown(!!).

Even out in the Delta Quadrant, in the episode "Unforgettable", Voyager runs into a race of people that emit an automatic Amalek(and everything else)-forgetting pheromone. Perhaps one of the lost tribes made it out there by then and it became a genetic adaptation after so much Torah study?

So, in conclusion, at least according to Gene Roddenberry and his successors, even 500 years from now, the memory of Amalek will still be busy being wiped out.