Promise Variant of Set-Packing
Suppose that there was a polynomial time algorithm $A$ for your promise problem, say with time complexity bounded by $const*|U|^a*m^b$.

Take an arbitrary instance of SET-PACKING (the original variant, not the priomise variant) and run algorithm $A$ on it for $2*const*|U|^a*m^b$ steps.
If $A$ does not terminate within this time bound, the answer must be NO.
If $A$ does terminate, verify whether the output produced by $A$ indeed is a feasible solution.

This would allow you to solve the original SET-PACKING problem in polynomial time.