I too am not sure but in general neoprene resists oil quite well, indeed is it is a common choice for seals/washers in oil+based applications I read somewhere.I would think that a natural oil would work, but I'm not sure whether it would damage the neoprene. The fact that I've never seen anyone do it would make me cautious though. If you have a dish soap that doesn't bother you, then that's the way to go. I don't think that just wetting the inside of the suit with water works very well. I have known a couple of guys that just jump off the boat with their suit and put it on while the rest of us watch in awe, but I'm not going to try it.
Also, have you considered glycerol / glycerine?? I sometimes use it as an anti-mist coating inside my mask (or spit!). And as a rubber lube e.g. on speargun rubbers. It is very slippery. I also use it to revive old, dried out watercolour paint pans. . I believe it is a byproduct of soap making (although fancy soaps often keep the glycerol as I believe it is a well known skin conditioner).