This.Any proper foam air filter oil should work. As long as the filter is squeezed out well and allowed to sit for a while before installation, it will not migrate out of the foam to any great degree.
I have no interest whatsoever in using foam filters in chainsaws. The cs590 flocked filter gets dirty very quickly and it would be a pita for me to bother with foam.
If it's making a mess it's over oiled.