On that train of thought, you should look into the Ostmen, the Norse who settled in Ireland. Many became Celtic rather than making Ireland successfully Nordic to the point that those who remained in their secluded cutouts like Dublin long after the Viking Age was over just stayed in separate parts of the city. Archeological evidence shows they built special quarters and didn't integrate, which carried over to later place names in Dublin. The British actually let them stay when they eventually conquered Dublin.

It is wikipedia I know, but it is a succinct statement

The Ostmen were regarded as a separate group from the English and Irish and were accorded privileges and rights to which the Irish were not entitled. They lived in distinct localities; in Dublin they lived outside the city walls on the north bank of the River Liffey in Ostmentown, a name which survives to this day in corrupted form as Oxmantown. It was once thought that their settlement had been established by Norse–Gaels who had been forced out of Dublin by the English but this is now known not to be the case. Other groups of Ostmen lived in Limerick and Waterford. Many were merchants or lived a partly rural lifestyle, pursuing fishing, craft-working and cattle raising. Their roles in Ireland's economy made them valuable subjects and the English Crown granted them special legal protections. These eventually fell out of use as the Ostmen assimilated into the English settler community throughout the 13th and 14th centuries

The larger influence was arguably the spread of Irish genes to Scandinavia due to captured and willing brides of Norsemen who brought them home.