I suppose my question is, am I being cruel to my baby and making him unhappy by denying him a dummy and the comfort that goes with that?
It's about understanding the compromises on comfort to sleep.
Children need comfort (in some form) in order to get to sleep right through to preschool age. So stopping the need for comfort around aged 3 to aged 5. That comfort does not have to be sucking, but sucking is one way to comfort. All ways require work and effort, they rarely just happen. The hope would be that as baby gets older, they learn to self-comfort in ways that don't need you (which dummy allows), not that they learn to not need comfort.
As mentioned in your other sleep related thread - at the moment your not offering your baby any (or enough) comfort to get to sleep. You seem to be making it hard for baby to sleep by not offering comfort methods, instead of easier.
So in terms of sleep - it's a case of picking your method. You don't have to use a dummy or sucking for comfort. Movement helps too. Or physical closeness like holding while asleep (can be replicated by swaddling) or cosleeping. Do if you don't offer sucking for comfort, you may need to double up on other soothing methods.
Most newborns need all these to feel comforted enough. That could involve dummy (for sucking), swaddle (for security) and swaying (for movement). It it could be feeding to sleep (for sucking), cuddling (for security) and rocking (for movement). Or any other ways to offer the comfort.
In terms of long term sleep habits, from the POV of parenting a newborn the idea is to Have A Plan. The idea is not to not comfort. It is about offering the comfort needed and then planning for the long term future and how you will gradual reduce the dependence on you so baby learns to self-comfort.