Linear types are stronger than FnOnce, in that a linear type must be used _exactly_ once. Rust doesn't enforce that if you pass in a function of type FnOnce that it is called.
So can you work around that requirement by just going:
if false
then <use my type>
else <do my things>
-- Using Haskell-like syntax, '-o' is linear arrow, i.e. lollipop
foo : Int -o Int -o Int
foo x y = if y < 0 then x else 0