Would be interesting to know where Kinghams obtained the name Thomas Cooksey from. This name does not exist in any Irish silver reference book including the very detailed one composed for the 2005 exhibition 'Cork Silver and Gold Four Centuries of Craftsmanship'. Nor does it appear in either of Douglas Bennett's books on Irish silver or in Cecil C. Woods treatise 'The Goldsmiths of Cork' (an old list but fairly comprehensive).
Cooksey is not mentioned in 'A Celebration of Limerick Silver' either or any other Irish Provincial silver reference source.
I don't think that is a dot. If it is, it's not in same position as the one on your tongs. Could be just a well used maker's stamp as I see that distorted T in another photo too.
Anyway, I should have noticed it before now but I believe the mark on your tongs is T.G not T.C. The serif is clearly horizontal not angled upwards. The only references to an Irish Provincial maker with those initials are:
Thomas Cooper Greaves 1781-1825 (Collecting Irish Silver by Bennett - Cork section - TG mark). Never heard of him and can't find any trace of him elsewhere.
Thomas Garde (briefly mentioned in Cork Silver and Gold and in this link:
viewtopic.php?t=14982 as a Cork jeweller) but nothing else showing for him.
Jackson's marks on Cork Plate, page 716, references a bright cut silver tongs with the marks TG STERLING TG and lists it as Unindentified. No dot on the mark though.
Maybe someone else here can offer more insight into your tongs.