There is no certainty that an airine would reduce its fares if APD was reduced, or zeroed or axed. It might keep them broadly as they were but retain the APD equivalent in order to improve yield instead of handing it to government.
In recent weeks the Westminster Welsh Home Affairs Select Committee has been taking evidence at various sessions - all available to view online - regarding APD devolution to Wales. They've heard evidence, both written and oral, from government ministers (Westminster and the Welsh Government), airport representatives (including CWL, BRS and MAN), airlines, taxation and travel 'experts' amongst others.
Ryanair said that APD is hampering its development at CWL, although I fancy they would say that about many airports as reduction/abolition of aviation tax is something the airline management has championed for many years.
As to the overall effects of APD abolition in Wales (effectively at CWL as it's the only airport of any size in the country), the committee was faced with the conflictng conclusions of two reports, neither neutral as one was commissoned by the Welsh Government and the other by Bristol Airport.
The Welsh Affairs Committee currently consists of ten Westminster MPs, nine representing Welsh constituencies and the other a constituency on the edge of Bristol. Having watched most if not all the evidence-taking sessions, it was apparent that one or two of the 'Welsh' MPs seem to have some misgivings about the idea of APD devolution: one was concerned about climate change and at least one of the others who is from North Wales wondered what would be in it for people living in that area given that most use MAN and LPL.
Nevertheless, I think it likely that a consensus will emerge in favour of APD devolution when the committee reports its findings which doesn't mean to say the Westminster Government will act on them.