Before you do anything, especially regarding installing another OS, make a backup image of your system so it can be restored in case of catastrophic failure.
Next, Linux doesn't need a lot of space, but shrinking a partition can be a problem, if there is not enough space inside the partition. Have you checked how much Windows is willing to shrink it, and is that enough?
Do you know if you are using an uEFI boot system on your laptop?
Linux will overwrite the Windows boot files when it installs, so check ahead of time how to get the Windows system back then make sure and have EasyBCD ready to fix it. I have not checked to see if there is a Linux version, but I do not think so. Here is a link to Link Removed and their Linux...