Do you feel the shimmy in the steering wheel or in your seat?
If it's in the seat, be aware it could be the drive shaft to the rear wheels.
The ujoints are not replaceable and the dealer no longer carries it.
You have to find a used shaft {probably ain't gonna happen} or find a shop to cut off the old ones and weld on new ones.
I have an '89 and couldn't find anyone who could do it, so i ended up taking the d/s out and running it in 2wd. Seems to work fine.
My problem now is the trany got low on oil and burned up 5th gear.
Still runs and drives fine, just can't use 5th.
Anyone want to buy it?

 

lol wut...? u joints are replaceable, cut off old ones and weld new ones...huh? they have a C" clip that holds them in.

 

Nope, not these.
Many manufacturers these days use non-replaceable u-joints.
Not just Hondas,
Subarus, and Mercedes I know of from 1st hand experience.

 

the "shimmy" could be as simple as uneven tire wear.