Hi Laura
Well done for training your horse so well to accepting a cue

I guess the first thing to ask is: Do you want your horse to continue to respond to your hand on his side, by moving away or are you happy with just the voice cue? If you don't want to get rid of the hand touch as a cue, then I suspect it would be confusing for your horse to learn that there are two different meanings for a touch on the side (ie one being move sideways, one being stand whilst I run my hand along your side)unless you can find a way to distingush clearly for you horse, the two types of touches, however at first he is likely to get the two confused until he learns their different meaning.
If you don't mind losing the hand touch cue for moving sideways, you could always extinguish the behaviour by ignoring the move sideways and being careful to not reward it in any way, then reward standing still with the hand on his side. He is likely to go through an extinction burst when doing this so the moving away will probably get stronger for a while, until he learns that it no-longer gets a reward. (I think you mentioned training him along these lines)
I have found with my own horse, that when he is unsure as to what behaviour I am after, I will get a demonstration of a whole range of behaviours that he has learnt, and as is typically the case, it is usually the behaviours which I would rather forget I ever taught him that raise their heads most strongly - such as trying to spanish walk my knee

(ouch!)
The above are just ideas that popped into my head when reading the post, as I don't know you or your horse I can only suggest ideas - they may be totally irrelevant to you and your horse, but I hope they might help you get to where you want to get.
MX
PS, sorry for my ignorance but what is 'cognitive dissonance'?