Not aware of any variation in law between NI and mainland - H.M.Inspectors of Mines covered both areas, the same inspectors covering Ireland (latterly NI) and parts of the mainland. The key post-war legislation regarding abandoned mines seems to be UK-wide in its scope - i.e. including NI.
Having caved both sides of the NI/Eire border (but not gone mine exploring on the Emerald Isle), I can offer the advice that there are far fewer caves (and presumably mine explorers too) and hence landowners are often genuinely interested (or even puzzled), but usually very pleasant and accommodating (but don't blame me if you meet the rare exceptions!).
May be worth making contact with the Mining Heritage Trust of Ireland (the national umbrella body which publishes a good journal) - they might be able to give some pointers. In the north, there are a couple of caving clubs active in the Fermanagh area that might have a foot in mine exploration in NI; best to ask on ukcaving.
Maybe post on aditnow about your impressions and experiences when you return?