Hi there,
Somewhere - in the UK - you can purchase 8 ft x 4ft sheets of 2 mm birch plywood. I know because I bought some for a model shop in Whitburn, Tyne and Wear a while ago - they cut if from an 8ft x 4ft for me - but the problem in now the shop in Whitburn has now closed down. I have been doing a bit of web search and I have come across this link but it seems it will only sell to the industry. If you contact them they may be able to let you know who they supply too.
https://www.specialisedpanels.co.uk/birch-plywood.html
Or they may even sell it to you - good luck.
When I was joining plywoods on real boats we used to feather them (taper them) but you wont be able to do that with 2mm thick ply. So, as suggested above, may be the best option.
John