What kind of SSD to speed up querying a lot of data?
You can't fix a performance problem by throwing hardware at it.

Even if you can find a fast enough SSD to handle the several-day query today, what will happen tomorrow when the data is bigger and/or you need another JOIN.

In many cases, a "several-day query" can be turned into a "several-hour" query by reformulating the query and/or adding a 'composite' index.  Or even "re-thinking" the problem.

Let's discuss the query and see if it can be sped up for $0.00.