I have the Simple human dish soap dispensers. I use them for dish soap and hand soap. They work perfectly well. There are two styles and I have both styles. Good luck!

No doubt- we are born at the right time to be good cooks! Now, to be more specific about my liquid soap. Any unscented liquid base will do. I use Dr. Bronners's unscented liquid soap, which I order, in quart bottles, from drugstore.com. I add 1.5 tablespoons spearmint Essential oil to a quart.(I also add a couple of glass marbles to the bottle, to help the oil to mix in.) I get my spearmint EO from Brambleberry.com. They also sell liquid soap base in gallon bottles. This may be better for you, since I imagine you will need larger quantities than I do. I hope this info is helpful.

Mask around the good tiles. First use a grout saw to remove all the grout. The key is to chisel into the soap dish, so you don't chip the adjacent tiles. Wear gloves and eye protection, it's dusty also. Then you can give them a gentle but firm 'wack' with a rubber mallet. Some will break off. Then using a hammer, and a 1/2" chisel, start chipping about a 1/2" from the edge. A pro would remove the grout and probably use and angle grinder to cut an 'X" or star pattern across the soap dish.

I'd score it with a carbide blade in an oscillating tool then break it up by gently tapping with a chisel. First take out the grout surrounding it, then see if there is enough room to slip the oscillating tool blade between the soap dish and the wall tile. If you can score from the back side it should be easy to break it up without damaging the tile. Alternately take out both the dish and surrounding tiles and make it a "feature" by using a colored or patterned tile around the soap dish if you can't find matching replacement tiles. Some makers (eg American Olean) have replacement tiles that are still astonishingly good matches decades later for their standard tiles.