I'm not familiar with the UUID module, so I can't provide you a simple answer. Looking over the debug log you'll see several messages starting with "# ===> Checking for" that tells you what the module needs in order to compile and link. Since Strawberry is using MinGW, I think Corion pointed you to a suitable library. I can't be sure, though, as I'm not using Strawberry Perl nor Windows 10.
I was able to install UUID on my Windows machine (Windows 8, cygwin perl 5.26) and it used libuuid, so I think there's a chance you can download, compile and install that library. After that it should be possible to try the UUID install again. (I've (briefly) looked at the source code for the module, and it looks like it can use the Windows UUID calls, so I'm not sure why it's not trying to use those.)
If you're not tied to that particular UUID module, you might try another, as there are several UUID modules available on cpan, including UUID::Tiny which (since it's pure perl) should install easily. Be sure to check the description of other UUID modules if you consider them, though, as they may have tradeoffs that you don't meet your requirements. UUID::Tiny, for example, mentions that it doesn't support "real MAC address in version 1 UUIDs, or an OO interface".
When your only tool is a hammer, all problems look like your thumb.