Some numbers from a T2-geared 'zerker. All parses are 600 seconds (+/- 3 seconds, depending on when I turned off autoattack), autoattack only, since we're only really concerned about the miss rate, and it was easy to gain the numbers while AFK that way.
webtools/magelo/character.php?char=MienParse one, every mod at my disposal on.
Mien -vs- Vlad: -- DMG: 962829 -- DPS: 1597 -- Scaled: 1597 -- Slash: 868479 -- Hit: 94350 -- Non-crit rate: 41.2% -- crit rate: 58.8% -- Attempts: 1343 -- Hits: 1120 -- Missed: 223 -- Accuracy: 83.4% -- Avg Hit: 859 -- Max hit: 1993 -- DMG to PC: 0
Parse two, removed +2HS mod (which is on both sleeves and gloves, replaced them with Glowing Chain from SMT to keep other stats relatively equal).
Mien -vs- Vlad: -- DMG: 816845 -- DPS: 1361 -- Scaled: 1361 -- Slash: 725295 -- Hit: 91550 -- Non-crit rate: 43.1% -- crit rate: 56.9% -- Attempts: 1333 -- Hits: 1036 -- Missed: 297 -- Accuracy: 77.7% -- Avg Hit: 788 -- Max hit: 1993 -- DMG to PC: 0
Parse three, replaced +2HS mod, removed +8% Offense (just to see what difference it might make).
Mien -vs- Vlad: -- DMG: 979145 -- DPS: 1629 -- Scaled: 1629 -- Slash: 883520 -- Hit: 95625 -- Non-crit rate: 40.2% -- crit rate: 59.8% -- Attempts: 1348 -- Hits: 1169 -- Missed: 179 -- Accuracy: 86.7% -- Avg Hit: 837 -- Max hit: 1993 -- DMG to PC: 0
~1350 attempts seems like a reasonable amount of swings to get things to average out, but the third parse wound up with a significantly better rate of both crit and accuracy. Depending on which number one likes better, or splitting the difference between them, no 2HS mod results in a drop in accuracy of between 6 and 9% at this stage of progression.