Will it hurt/corrupt a savegame if you use/save it on different computers?
Currently I'm playing through the game on my own system, but I would also
like to transfer the save to my parents' laptop as well. Creating a perfect
character, so I was wondering if there are any risks if you keep transferring
a savegame between computers?

Thanks in advance!

Not likely, but you need to be sure that any mods you're running stays the same between computers, because THAT can cause issues.

As Marss said, only if your load order isn't identical. Other than that I can't think of any issues, unless you messed with the ugridstoload setting in the .ini file. That's the one ini setting that can cause problems if it is suddenly different when you load up a save. But unless you really went into the ini file to change it, that shouldn't be an issue.

I'm not using any mods and haven't changed the ugridstoload setting in the ini file.
All I've changed in the ini file (on my own quad core system) is the one to force it
to use 2 cores. The laptop is a dual core so I guess I won't have any problems then,
thanks!