Will kontakt player still work if I place it in my external hardrive?  I am running low on memory in my PC's hard drive. 

You can place the VDL sample library anywhere you like. Some people have even put it on a USB flash drive. If you move it though, make sure to tell Kontakt Player where its new location is.

Otherwise, the only problem you may have is that the playback performance may be diminished if Kontakt Player can't access the sounds as fast as it used to. External disc drives tend to be a slower that internal ones.

The Kontakt Player application doesn't consume too much space. Plus, the plug-in version needs to be living within certain folders to work properly. So I'd advise against running the standalone application, or the plugin from an external drive.

As Hugh mentioned, you can house your VDL library on an external drive, but you'll need to direct Kontakt Player to its new path once you've moved it. If you don't, you'll get a ";Samples Not Found"; error.