Liquid stylus cleaner without solvent

@whart is correct: Ortofon recommends using just the stylus brush, without any liquid.

Last Stylus Cleaner (it comes with a very dense circle of short bristles on a plastic handle with which to apply to the stylus), followed by an application of Stylast. I’ve been using both since they were introduced in the 1980’s.

If to look from chemistry side in order to dissolve oil based contaminants you can't do it with pure water. You have to have dispersing agent and alter pH to alkaline side in order to make it work faster. Also IMO water based solvent for regular use is better as it's not drying so fast as alcohol based so you can remove residue without allowing it to dry on stylus
For the very sticky contamination I do use isopropyl lab grade but I am soaking tip into it several times. But it's special cases and it not always make good results. 

The concern is only for styli that are glued on. As for what kind of solvent would attack the glue? That depends on the type of glue being used.
Alcohols will attack epoxy. Acetone will attack cyanoacrylates. I have not been able to determine what type of glue is being used. There are some very tough adhesives out there that are rapid curing. The adhesives used on solid surface material (Corian) are a good example. They are two part like epoxy and cure within minutes. Very little will attack them. There are many adhesives that are perfectly stable in water. If water attacked epoxy the entire fiberglass boat fleet would be sinking.  

lewm is correct. Water is a weak polar solvent. The Lyra stylus cleaner is water based. I have a bottle and it seem to work fine. But do you really need a solvent? I think Cleeds makes a very valid point. If your records are clean then what is there to worry about? A very soft artist brush will knock any incidental dust off just fine....as long as the dust is dry and not carrying any lipid like pollutants produced by from cooking and smoking various combustibles. You mix up dust with water and you get cement. Mix it with cooking fumes and you get tar.  If this gets on your records then you stylus will collect it like a plow collects snow. A dry brush will not get this stuff off. I am sure there are solvents that are safe to use. When you see these blanket statements there is usually a liability issue underneath. Problem is that without knowing the exact adhesive used it is hard to know what is safe. One thing is for certain, the gel or solid stylus cleaners are not. I know of two examples of people loosing styluses using gel cleaners. If the motion is anything but straight up and down the lateral stress will break the diamond off. Whatever glue is being used it is quite brittle. You can see that in the picture I took of the missing Clearaudio stylus, a jagged and sharp fracture line. 

If your environment is clean, no smoking or cooking and your records are clean then all you need is a soft brush which is what Peter Ledermann recommends. Mostly that it all I use. Unfortunately, life is never perfect and occasionally I will see some adherent goop on the stylus. I have always used a 50% solution of isopropyl alcohol in water but switched to Lyra cleaner after my Clearaudio stylus disappeared. If we can find out what adhesive is being used from one of the manufacturers we can know exactly what is safe. My guess is that many of the manufacturers also have no idea what is being used. It appears the cantilever assemblies are manufactured elsewhere, made to order and supplied ready to install. 
Perhaps we can get Peter Ledermann or Jonathan Carr to comment on this subject. 

I can explain using a few images of my carts on macro lens (after cleaning):
With press-fit diamond like this it’s OK to use liquid stylus cleaners (a few drops on stylus cleaning brush). But with this type diamonds glued to the cantilever I wouldn’t use liquid cleaners! If you don’t want your stylus to fell off do not use liquid cleaners, use dry brush or onzow.