//I know that if Mr RR dies within 7 years there will be tax to pay, but I'm presuming that will be for the cousin to settle, not Mr RR's estate, is that correct?//
No. If Mr RR dies within 7 years the 23k will be taken off his nil rate band (currently £325k). All lifetime gifts within 7 years reduce the nrb. Once the nrb is exhausted with lifetime gifts, then the allocation of tax becomes a headache. However, this may be irrelevant if he leaves it all to you.
It may be worth exploring the issue of a Deed of Family Arrangement. I do not know enough about Irish inheritance and taxation law and cross border taxation to be able to advise on this. You could take some advice to protect your own position and then deduct the cost of that from the money you intend to pay the cousin.
I found this:-
http://www.ohanlontax.ie/downloads/DisclaimersandDeedsofFamilyArrangements.pdf - but you may be out of time to do a Deed of Family Arrangement in any event.
Sorry if my answer duplicates other answers, I didn't have time to read all of them and just answered the question.