It shouldn't be an option for him not to reveal how much tax he pays.
No-one else has to reveal how much tax he pays - in the UK it's a private matter between an individual and HMRC. Some politicians decide to reveal it but they are not required to do so.
The Prince of Wales apparently pays the highest rate of income tax. He doesn't need to tell anyone that, and doesn't need to tell people how much.
I do think that paying tax on private income should be compulsory rather than voluntary for the Royal Family.
With regard to scrutiny of the finances of the monarchy: it's possible there needs to be more, or people need to be clearer about what scrutiny there is.
There is scrutiny of the Sovereign Grant by the National Audit Office and the yearly accounts are a public document. (SG Act 2011 pulled it together - previously looked at by several different departments.)
The Duchy of Lancaster accounts are presented to Parliament and are a public document (Duchies of Lancaster and Cornwall (Accounts) Act 1838.)
The Duchy of Cornwall accounts are presented to Parliament and are a public document.
They are discussed regularly in the Public Accounts Committee.