My school does not have a guidance counselor. Would I nominate my dean or form class teacher or a member of senior management (deputy principal) for this role instead?
Yes I would nominate any of those for this role or potentially your school’s careers advisor or even principal.
I would suggest you ask the person who you are closest with out of all of those options.
As Brendan has said, the most important factor is how well they know you. Under the condition where they all know you equally well, you should choose the most important person in your school, such as your principal (then dean, then head of department). You should not be using an academic teacher who teaches you just one subject.