Unless you've basically hit the attack cap on the mobs you're fighting (which, unless they're wimpy, you generally won't), 20 attack > 4 STR for WS. Particularly for MNK WS, since the secondary mods for STR are relatively low.
As a general rule, when macroing for WS on any melee job, you typically sacrifice *some* acc gear (enough that you can get away with it and still regularly land most/all the hits on the WS) for STR and secondary mods, while maintaining or increasing your attack (although if you can swap a low attack piece for a high STR piece, go for it).
How much to care about macroing for secondary mods depends, really, on just how strong they are. A 75% mod is definitely worth macroing for, 50% is worth it if you're not sacrificing too much, 30-40% is more to the tune of "if you can get the secondary mods along with other good stuff, cool, if not, don't sweat it", and 10-20% you really shouldn't even be thinking about them because they'll do next to nothing.