Hi kicksave98,
Per Use iCloud Music Library on PC:
"WARNING: After you turn on iCloud Music Library on a device, all the music that’s currently on the device is deleted and replaced with songs from iCloud. Also, you can’t use iTunes to sync music with the device. You can add songs to the device only by downloading them from iCloud." (emphasis added)
As the songs are not in the Apple Music Library and you indicate you do not wish to upload those tracks to your iCloud Music Library, it would be necessary to turn off iCloud Music Library for the device in question. Note that in doing so, should you turn that back on in the future per the above warning, "all the music that’s currently on the device is deleted and replaced with songs from iCloud" which would result in the removal of synced tracks.
As an alternative, you may try the file sharing option as described in Transfer files between your PC and devices with iTunes to see if it's possible to transfer those songs directly.
Regards.