Diggis
As @[deleted] absolutely correctly suggests, cursor themes are nothing else but icon themes.
It is possible to copy by hand the entire subfolder with your preferred cursor (icon) theme from /usr/share/icons folder in a previous distro into /usr/share/icons folder in another distro. Copied cursor theme will be available system-wide.
It applies not only to Solus Budgie but to any distro and any DE.
Obviously, if a theme is upgraded in a source distro, then hand-copied theme won't be upgraded in a destination distro. Well-established, stable cursors are almost never change.