As I understand, if you have a thicker cream, you are not allowed to smear it on on Shabbos, but you are allowed to dab it. If you dab on the cream and after a few minutes you want to wash the cream off your hand, is that permitted despite the fact that inavertantly some cream may stay back, and on that cream you are smearing a solid into a liquid

Yes, you are allowed to wash the cream off your hand. Explanation: 1. The Mishna Berura relates that some poskim hold that, although one may not melt snow or ice, there is no prohibition to melt soap. The reason for that distinction is because ice turns into water which can be used for drinking and is similar to fruit juice. If we permit drinking the water from melted ice, someone might decide it is permissible to squeeze fruit juice. That would be clearly prohibited on Shabbos. Soap and skin cream are never used for eating or drinking and are therefore permitted. (Mishna Berura 326:30) 2. A person has no intention of melting the cream and making a liquid, rather the intention is merely to wash it off. 3. The liquid that was 'created' by washing it off gets lost in the sink. 4. There is a 'tzorech' (meaning a need) to take it off. For Sources to 2-4 see the Mishna Berura (320:32,39,41) By the way, you write that "if you have a thicker cream, you are not allowed to smear it on on Shabbos". Some permit using thicker creams on Shabbos in certain circumstances (see Shemirat Shabbat Kihilchata, 33, comment 64) All the best