It also depends on how you define iTunes. Apple includes iOS music app as part of "iTunes", and by far there is no app that can transfer music files from iOS device to Apple Watch except Apple's own music app.
So, while you can load music from computer to your iOS music app without using iTunes, you may have no choice to load music to your Apple Watch without using iOS music app.
PS: If you have Apple Watch series 3, you have up to 8GB to store your music depending on your model. It is no longer 2GB.