I believe the Scottish successor would be James Hamilton either the 2nd or third earl of arran.
Aye, it would be James Hamilton 2nd Earl Arran and sometime Duke of Chatellerault, but his eldest son is already crazy and that may complicate matters. Arran himself is also quite old (he died in '75 IOTL) and he may have been imprisoned at the time of our POD.
The Lennox Stewarts had also claimed that they were the rightful successors- they contended that the 1st Earl of Arran's marriage was invalid and that they were the rightful heirs as descendants of the 1st Earl of Arran's sister. Was their status as heirs confirmed/acknowledged by Mary when she married Darnley?
But Matthew Stewart 4th Earl of Lennox is already dead and his son Charles is in England (and his mother is probably focused on getting him the
English throne). There are some brothers of Matthew floating about but I'm not sure what they're capable of.
There's also royal bastards around, but I don't know if anyone would go for that.
As for the English succession- if Lizzie has her OTL lifespan there's 30 years of potential butterflies there (different kids born, different possible successors falling into disfavour with Lizzie and facing imprisonment, longer/shorter lifespans for important figures etc.). But the obvious candidates are 1) Charles Lennox/his offspring; 2) Edward Seymour, son of Catherine Grey (though he's officially a bastard); 3) A Stanley descendant of Margaret Clifford (IOTL this line was represented by Anne Countess of Castlehaven in 1603)- but Clifford fell into disfavour with Lizzie later IOTL, and her sons were suspected of Catholic sympathies/caught up in Catholic plots or somesuch. A Hastings (Earl of Huntingdon) was floated as a potential successor during Lizzie's brush with smallpox in the 1560s, but their claim is remote (deriving from George Duke of Clarence).
Not to mention that in England, Mary of Scots is still alive but has just been directly linked to a plot to kill Elizabeth, and while this isn't the first such plot, this is the first plot that Mary of Scots directly signed off on. Now theoretically, Elizabeth could launch an intervention to put Mary back on the Scottish throne, the question is... would she?
I s'pose it depends on if you can conjure a scenario where a Mary reinstalled on the throne by English influence better serves England's interests than whoever seizes power in Scotland, and reinstalling Mary is worth the cost of intervention (military/financial/whatever). Wouldn't a significant proportion of Lizzie's councillors be opposed to releasing a potential Catholic heir to the throne?