Is "let go your hand" grammatically correct?
Wherever "let go of your hand" is used, can "let go your hand" be used in its place? Is there any difference at all?
Solution 1:
"Let go your hand" is grammatically correct, but archaic. See Shakespeare's Julius Caesar: "let slip the dogs of war."
Solution 2:
No, you shouldn't drop the prepostion of in the expression let go of.
The expression let go is used for ceasing employment, so the result could easily become confusing or misleading.
Solution 3:
There is nothing grammatically incorrect in your phrase.
Consider thus:
Let your hand go.
It is the same, where "your hand" is the direct object of the verb "let". You've simply inverted part of the sentence, which has no bearing on the grammatical soundness thereof.
It does sound a bit odd, all the same, at least, to me (native US English speaker) it does.