If you are not comfortable in attempting to clean and conserve the coin, then it would be best left to the professionals! If you send the coin to NCS, they will conserve it, then it can be sent over to NGC (same Company just different departments and services) for certification, grading and definitely ask for attribution for the Variety. I am unsure as to whether there is a known Variety of a 1793 Flowing Hair "Chain" Cent without the "bars and vines with leaves" on the edge as I do not have the reference books on these rare coins nor can I readily find anything online. NGC should be up on all of the different Varieties for the 1793 Flowing Hair "Chain" Cent but if not, they will likely consult some experts. If in fact, it is missing the "bars and vines with leaves" on the edge and if it happened to be an "AMERI." Variety or the one with periods after "AMERICA" and I believe "STATES", then you could have a coin that is worth a lot more than $4,000. In any case, without some conservation and cleaning, you will likely never know which Variety it is and how valuable it actually is or could be!
Frank