A Slug Catcher,finger type,in order to be cleaned has to be designed and built to include the access ports (blind flanges for instance) for cleaning.But before cleaning you have to have also provisions for inerting or steaming out the Slug Catcher after depressurisation before opening any flange.Then depending of the size of the fingers and access flange you decide to use a flushing hoses,mechanical or chemical cleaning by your own maintenance team or look in your area for a specialized Contractor in Oil & Gas facilities maintenance.
The only time I've seen anyone try to clean a slug catcher in service, they used a steam hose through a temporary lubricator off the liquid-dump drain line. Then they went back with a downhole camera to see if they were effective - they weren't.
I design slug catchers and drips with a blind flange on the head end, but with the shape of the vessel, it is really difficult to clean the toe. Most likely it would be cheeper to cut the toe-end off, shovel the sludge, and weld the end back on. Cleaning it without major interventions would most likely result in excessive system down-time (and I've seldom seen a constructin bill that approached the lost-production bill for a week-long outage to try to clean a slug catcher in place).
I wouldn't expect the Thomas Register to have a category of "Vessel Cleaning". I'd approach it with my regular construction contractor.
Most offshore platforms lack steam. A few oil service companies perform chemical cleaning and many perform general cleaning. Depending upon the location, check with international companies like Halliburton, BJ, Schlumberer, etc. or local oilfield service companies found in the yellow pages, etc.