PROVIDED you do not:
1. use HEAT
or
2. use MECHANICAL (e.g. sandblasting, sanding, etc)
means to remove paint, and do not get the stripper INSIDE the tank (which would be bad for YOU, not the shop) its perfectly fine.
Chemical strippers, in fact, are the only acceptable way to remove paint from an AL tank. You must also NOT use heat to "cure" any replacement paint. Heat WILL change the metallurgical properties of an aluminum tank to the point that it is unsafe.
A re-hydro is not necessary unless there has been mechanical or heat stress to the tank in the process. If there has been heat stress then the tank is junk even if it passes hydro, as the changes that this causes may not cause the tank to fail a hydro inspection even though it has been rendered unsafe.
Aircraft paint stripper is MADE for use on Aluminum - that's what most aircraft skins are made out of!
In most cases a sprayed-on logo cannot be properly removed from a painted surface. If you manage to get it off (there was no chemical bonding between the paint layers) there will usually be a "shadow" where the painted-on thing was, that will still show what was previously there!
The best bet is to strip the tank entirely; if they're Aluminum (and it probably is if they were former dive shop tanks) just strip it bare and use them that way. I frankly think that the "bare" finish holds up better cosmetically than paint anyway; only Catalina does a reasonably-decent (read: durable) job with their factory paint on AL tanks, and you will not be able to duplicate their work easily if at all.