i use a generic version of this stone. bought for $10 or $15. i wet the stone and then sharpen with both sides of the stone. leaves my edge sharp enough to cut paper. Welcome to Mountain Sports outdoor clothing and gear for backpacking, kayaking, skiing, camping
How sharp do you need/want a splitting axe to be? Can it be too sharp and risk folding the edge over? Seems like the file might be the best approach?
If you put too steep an angle on it , it would definitely fold or chip. I get most of my stuff from people who would rather throw it away than put an new handle on. I like putting them back in service and maintaining them over cheap big box stuff. That doesn't mean they don't get used hard- just clean them up when time permits. Some heads a file wont scratch and have to use a stone. Emory in a drywall hand sander for safety reason is more for final clean up.
Out of the box, one time maybe with Dremel & sanding drum. After that, always splitting up on a block, edges stay sharp. No fiskars here.
High speed angle grinder with 60 grit sandpaper or a flap disc will make axes scary sharp in a hurry without heating up the metal.
easy way to sharpen an axe is with a file in a vise, using oil on the file from time to time and wiping off the metal particles. the thing is you not only sharpen your axe or hatchet, but when you first get it, the face back from the edge frequently needs to be profiled with the file. there are production ways to go about this but country boys do this with a file. you don't want the profile of the axe too convex hence a bit of dressing. after i've filed or ground tools the lazy man's hone is to buff the wire edge off. yes you have skipped some steps but you have sharp, quick.
Chucker is right on about getting the part behind the edge properly profiled. Not just on a new axe, either. Every time you sharped, you move the edge back just a wee bit and eventually, you'll be back on a thicker part of the axe and you have to remove some metal from behind the edge as well to keep the overall shape proper. I use a file and diamond hones depending on how much metal I need to remove and how sharp I'm going for. I don't need more than a file for a splitting axe, but I like a cutting axe to be sharper so I use the diamond hones. In general, the smaller the cutting instrument, the finer edge I put on it.
I use a 6" dia-sharp DMT diamond stone fine grit. Forward movement from edge toward the poll. I finish with a extra fine diamond stone in 1200 grit.