I've never done the oven cleaner/cherry wood stain thing.
But for something to neutralize the lye in the oven cleaner, I use wood bleach (oxalic acid) very dilute on wood (walnut) that has had the oven cleaner trick done to it simply to remove the oil.
(Don't use laundry bleach!)
Wood Bleach is made for wood pre-finishing and it does even up the color nicely.
In that case it also does what it is supposed to do,,lighten the wood.
On walnut, it brings back the 'walnut color', though a little lighter of course. The lye treatment will leave it with some strange colors sometimes,,nothing as usable or desirable as the cherry wood look.
I do not know if you could also use it on the lye darkened cherry and still have enough color left after treatment to satisfy you,,
Or..It may not lighten the 'stained' cherry wood at all being oxidized with the lye instead of a color stained surface..
Worth a trial on a piece of scrap I'd guess.
I use a tablespoon of the wood bleach crystals in a quart jar of water. Warm the contents in the mickey-wave for 30seconds or so. Apply with a brush to the still wet wood from the rinse off of the oven cleaner.
Rinse again after applying wood bleach.
It'll sting your hands even diluted, so handle with care and watch the eyes.
Maybe it's a mute point altogether,,,, but neutralizing the lye seems to help in the finishing process on walnut.
I'd rather neutralize something that heavy a base that's been applied to the wood than not.
Some nice looking stocks here,,,might have to look into a piece of cherry next time..