From the study of my own Disney family tree for over 50 years I have registered a One Name Study with GOONS in the UK and have over 15 distinct as yet unconnected Disney family groups in the UK.
The availability of yDNA tests should help to find out if the family groups are linked or not.
The project is open to anyone, worldwide to join the yDNA project (ie a male with the surname Disney) yDNA tests can help with family history research in many ways. Find who you are related to.
If you can't find a document to prove a common ancestor a yDNA test could provide evidence.
The project now has 6 well established Disney family trees,
The Norton Disney family, now linked by DNA the Keyworth family which spread in Derbyshire and Leicestershire.
The Irish Disney family from Stabannon.
Walt Disney's family.
A Suffolk family that has a branch that emigrated to Maryland in the 1600's
A family from Devon and Somerset originating from the D'Assigney family in Jersey.
A family in Australia from Elizabeth Disney transported to Tasmania with her three sons in 1839. A yDNA from a male member of this group would perhaps be able to link this family to others.
Husband was William and they were Catholic suggesting a possible Irish connection.