It's possible to obtain Epona without getting either Epona's Song or racing Ingo by touching one of the three loading zones that are normally only reachable by riding Epona, triggering a cutscene showing Link jumping into Hyrule Field on Epona.
One of the ways to get Epona during normal gameplay is to jump over the lowest part of one of the perimeter fences while you race Ingo.
It is possible to hit the same loading zone simply by doing a staircase hover at the same location. This will give you enough height to be able to backflip over the fence.
As night and child only, there are 4 gold skulltulas in Lon Lon Ranch that you can get. Normally, 2 of them requires the boomerang because they are way too high for a ground jump or a jumpslash. However you can still do a hover to reach them.