I setup bspwm on top of budgie so I had them both at login. You should be able to toggle an icon right where you type your password in the login greeter. After you install hyprland that is.
Your question is can you install a WM in a partion you made for it? I don't think so. At Solus you only get your choice of 4 distinct downloads, none of them a WM.
Can you have a WM without a DE?
Can't say with certainty but someone else can.
EDIT:
can you run them together w/xfce? looks like yes
reddit.com/r/hyprland/comments/17dvlzo/optimal_way_to_install_hyprland_on_endeavour_os/