This is valid for child porn but let's assume that the illegal content is something like private photos of someone consuming drugs, for example. While it might be illegal to do so on many countries there are countries and even US states where you can consume drugs. This is just an example .... If it's something like this the OP can just mail the drive to a country where the "content" is allowed and ask for them to recover the data he wants keeping aside the data he doesn't want. Or if it's just a few bunch of files that are really needed the OP can ask for the ones doing the recovery to post it on something like a private FTP server, etc .... This way the possible illeagal content will not transit to the country of origin where it is illegal and it will stay on the country where the recovery is done and there it will be leagal.

Well, my point is .... I guess it will depend on what the content is.

and likely all the hard drives in your lab being taken into evidence.

All the HDDs ?????
The entire business which includes all your computers (and everything in it (PC3K Etc. Etc.)) can be taken away for investigation, that can take a long time until you'll get it back.