I looked into doing this using the existing hydraulic pump on my tractor and it turned out there would be a trade-off somewhere for sure.
The bore of the cylinder makes a lot of difference. (With a pump of a certain number of gallons per minute, increasing the bore of the cylinder will get you more pressure, but it will travel slower.)
You can figure this stuff out with a bit of math, but you have to find out how many cubic inches in a gallon first, which I forget.
Say the cylinder is 4" diameter. To travel 24", you need Pi*r*r*l = 3.14 x 2 x 2 x 24 = 302 cubic inches of oil, however many gallons of oil that is. But with a 3" cylinder you only need 3.14 x 1.5 x 1.5 x 24 = 170 cubic inches.
Next find out how many gallons of oil your pump can supply per minute and you can see how long it takes the cylinder to extend 24". When I went through this exercise with my 5 gpm pump (or was it a 5 cu ft/min pump? - can't remember) it turned out that it would take 17 seconds to extend, if I remember right. Don't forget the cylinder has to return too.
Then there is the force the wedge will apply to that monster elm stump that has been taunting you for three years. It sounds pretty good, until you check out the force versus speed tradeoff. So again with the 4" and 3" examples - let's say your hydraulic pump operates at 2000 psi. For the four inch piston, the force will be 3.14 x 2 x 2 x 2000 = 25132 lbs, or 12 1/2 tons. For the three inch: 3.14 x 1.5 x 1.5 x 2000 = 14137 lbs, or 7 tons. (Not much!) So you think - let's just move up to a 4 1/2" cylinder. 3.14 x 2.25 x 2.25 x 2000 = 16 tons. Now we're talking!
But 3.14 x 2.25 x 2.25 x 24 = 380 cubic inches of oil, which means that by going from a 3" to a 4 1/2" cylinder, the travel time will be 380/170 = 2.24 times as long. This is really significant; we're talking about the difference in cycle times of say 40 seconds versus a minute and a half.
So if your pump isn't too high a volume you might want to consider a pto pump, or a belt driven one, for the logsplitter, which of course adds a lot to the cost.
Jim W