AIUI, they're doing a documentary about how the war affected them and their careers.
Ardiles is an Anglophile, and has never - as far as I know - expressed any support for either side in the dispute over the islands; rather he's on record as lamenting the fact that the two countries he loves went to war. (IIRC, the Lt Ardiles shot down and killed on 1 May 82 was his cousin). He went on loan to Paris St Germain, hated every minute and returned to Spurs in 1983; at least two of his sons have spent almost all of their lives here.
Villa - again as far as I know - hasn't expressed a view on the matter of the Falklands, although he was forced to withdraw from the 1982 FA Cup final (or was it the semi final?) because he was being accused of treason by Argentines for continuing to play with the enemy. He is particularly vitriolic (at least in the British press) about the nationalists who came out with this (suggesting that their parents may not have been in a state of wedlock). His daughter holds dual nationality and he still clearly identifies with Spurs, since when Arsenal played Barcelona in the Champions League he was interviewed and said that like any good Spurs fan, he wanted Barcelona to win.
I daresay that the view taken was that neither of them is likely to try to do anything akin to the stunt pulled by the hockey player two years ago, or to be found expressing virulent hatred of Britain, or coming out with propaganda which Mrs Kirchner will just love.