Be careful with this - I've seen pH meters that specifically state in the instructions NOT to use deionized water for cleaning.
Also, as a general rule, if you are going to clean your pH meter with a wipe, towel, whatever, you need to be very gentle as too much friction can cause static and mess with the electrode.
The pH meters I worked with did not instruct not to use deionized water. The point I was trying to make was that the cleaner needed to be rinsed off. It's not to be left on the probe, no matter what is used to rinse the probe.
Also, yes - Kim Wipes are meant for delicate tasks, and you do have to deliver the cleaner to the probe as it is a liquid. Therefore, the Kim Wipe (with gentle usage) is the way we went about doing it.
I'd hope that the user already knows how to use their pH meter, and has read its instructions. However, to the OP - yes, there are cleaners available which are specifically for oils/greases.