I replaced the bushings on our past 126 body, without removing the sway bar.
Its a bit of pain, you'll need some prods and patience but you can definitely do it. The bushings are held-in by U-brackets that are held down by two bolts, if I recall correctly that are attached to the body.
Take the U-brackets off, this gives you "some" play to wiggle the big rubber bushings out. A little silicone lube would definitely help.
'03 E320 Wagon-Sold
'95 E320 Wagon-Went to Ex
'93 190E 2.6-Wrecked
'91 300E-Went to Ex
'65 911 Coupe (#302580)