As I understand it, Welsh actually derives from the old German root word for foreigner. Ironic given that the Germanic invaders were the foreigners. The self identifying word for the Romano-Britons was ‘Cymri’ and echoes of that can still be found in their western strongholds of Cymru (Wales), Cumberland (the Lakes region) and at more of a stretch, Kernow (Cornwall).
Cornish is now an official minority language in the UK and is growing strongly after dying out in the 60’s. A group of far sighted individuals spent a long time interviewing and taping the last fluent speaker before her death and have used that work to rebuild the language.
I think you are right about the origin of Welsh. It is supposed to be related to Walloon (the French-speaking Belgians), Wallachia (as in Romania), and Vlach (Balkan shepherds whose language is similar to Romanian). In each case they are the people who lived under Roman rule, from the standpoint of the Germans. I think the Polish word for “Italy”/”Italian” is related.