Ideally if there is enough homology between query and subject you won't have much of an issue with similar domains leading to false positive results.
However hmmscan won't fix this if you're only searching for a single domain or if the conserved region you select shows up in other places. Depending on what your enzymatic domain is, it could be present in other proteins. In other words, the opposite case of what is described by OP could be true, the enzymatic parts match but the other regions don't.
HMMs are a more advanced model, but the general concept is the same as PSI BLAST. You're basically searching with a 'fuzzy' representation of a group of sequences rather than a single sequence.
I think your best bet would be to maximize alignment length or confirm each BLAST/HMM hit with a global aligner (e.g. clustalo).