I would vary the molar ratios of isothionates to protein amines and empirically determine what ratio works best. Or if you know how many amines are facing the solvent, then you can always add a molar excess of protein, but then not all of the protein molecules may become labelled.
Modification of accessible lysine side chains by isothiocyanates is probably going to reduce the activity of the enzyme, so try to keep the labeling to the lowest stoichiometry possible. Active site lysines, if any, will probably be the most reactive if they are accessible, and modifying them will inhibit the enzyme.
Consider modifying exposed Cys residues, if any, instead. There are usually few of them, and they can be selectively modified with maleimides or iodoacetamides under neutral pH conditions in protein-friendly buffers like Tris and Hepes.