Basically I’m trying to avoid having to do 100 M+ before raid and I’m swapping from healer to melee.
Is there an easy-to-get weapon that is ilevel 200+ with 9.1? If not, what’s the easiest way to get one?
Korthia armaments, but it’s rng. Otherwise 190 off the ah
Yes, and no.
I would guess you have stygia, and that can get you Korthia Armaments (I think that’s the name) which you can mail to your alt to create a random item.
I sent 20 to my unplayed hunter alt and ended up with a bunch of duplicates, but I did get enough non-duplicates to fill out 11 gear slots, including a weapon.
Of course that’s 1 weapon out of 20, so I wouldn’t imagine the odds of a weapon are particularly very high.
Get lucky with Korthia armaments. I managed to grab a staff and upgrade it to 220.
if you’re at 40+ renown WQs should give a weapon in the 194 - 207 range
Literally just go do Korthia, and the rares in the maw.
Shadoweaver specifically drops a staff (ILvl 207, upgradable to 220)
Hey love,
Recently geared this bad girl up.
If you are willing to slog through 4 m0 runs you get a heroic nathria item this week maybe you’ll get lucky! Furthermore the campaign does give a 187 (not 200 but it’s better than the 140 you get from story). Have a 220 offhand and that 187 main hand now 
Edit ANOTHER IDEA ;
Honor will carry across the reset and you can use that to buy a decent weapon off the bat in like two days. Farm honor hard and fill your empty slots.