This is a unlikely source but Fiskars makes a pull through axe sharpener. It's not like regular ones with two ceramic or carbide rod, but two rotating wheels that work better and not easily clogged. It has a handle but you can chop that off to use head only.
YMMV, but I have to strongly un-recommend this item. I bought one, and it was appallingly awful. I couldn't believe Fiskars would put their good name on something like this. There are much better options for the same dollar IMO.