How to change user running audits mssql
despite having never done this before


that's not a problem at all - I just would recommend you do all this on a test server first. the whole process. then you do it in live. 



This is how I would do it: 


you create the domain account sqlaudits as you mentioned and take note of its password as you will need it later on
create a login for sqlaudit on the server you want to audit
grant sqlaudits all the permissions it might need: on that server

Check the permissions for altering an audit:

a)To create, alter, or drop a server audit, principals require the ALTER ANY SERVER AUDIT or the CONTROL SERVER permission.

b)Users with the ALTER ANY SERVER AUDIT permission can create server audit specifications and bind them to any audit.
run ssms as a different user using the sqlaudits account credentials


to run ssms a different user press the shift and right click on the ssms icon and that will give the options below:



Now you are sqlaudits and the objects you create will be technically owned by you