Amines are one of those fluids that seem to be one of those automatic 'stress relieve' triggers.
The ethylene plant I worked in removed CO2 from the feed ethane using MEA. We ended up having to replace both CS towers, CS heat exchanger shells and all the CS piping due to cracks. The cracks were extensive enough on the regenerator we had to reduce the PSVs to less than 15 psig to make it a non-code vessel. The original design did not call for stress relieving of carbon steel though I don't know the reason.
You could try talking to the amine vendors and see if they can supply you some contacts with people using the same amine you are considering to remove only CO2 to see what their experience is. Personally, I would be leary of not stress relieving the piping and equipment.