Would you want to access/sync the iPod from both of the computers? I'm not sure if you can do that, but I think if you want to store your music in the cloud (have you got a OneDrive account or would it be in DropBox or something?) you can probably just change your library location to be a folder in OneDrive (you can definitely select OneDrive folders from the library select menu, at least). So that way all you'd need installed on your Surface itself is iTunes.
Try that, and if it doesn't work then you might have to check out the Symbolic link stuff below:
You might be able to make it work using
Symbolic links (basically a fancy shortcut) - I had to set them up on my Surface to get iTunes to save my iPhone backup to my external hard drive because for some reason you're not allowed to officially change where it stores your backups, so you could probably do a similar thing with your whole library.
iTunes is also pretty useless at handling libraries saved on external drives (so if you ever even
dare to start iTunes when the drive isn't connected it'll simply change the library location back to it's default, but not tell you), so you can get a script that you can run that will always check if your library is there before starting iTunes to avoid that disaster (I've had far too many times where I'll have ripped a new album into iTunes without realising that my hard drive is turned off, so it makes a brand new library on my C drive and copies the new songs into that library, and then when I notice a few months down the line that it's moved my iTunes library I've got two or three different incomplete libraries scattered around
).
I can't find the link to the script at the moment but if you want it I can post it on here.