Since it's "watch only", there is no need to fear, but if the email is one you use for other sensitive matters, then I would suggest you change the email in places where you can be compromised. As other users have already said, exposing your address is not a problem, but the email can be used to send phishing links. It would be best if you could change the email to something else, if possible. At least things that can be compromised.
You can actually still use the email even though you would be getting phishing emails. As long as you don't click the emails and share sensitive details, then no problem, but if you want to be more secure, you can change the email.
I don't think he necessarily needs to change the email address linked because once it's exposed, then it's already exposed. Changing the email address to introduce a different email address will only be amplifying the damage caused already because the scammer will now have two of your emails which will also increase your chances of falling to their phishing links that would now be sent to your both emails.
You can disconnect the email address from other of your important areas and only allow it to operate with the exposed address and nothing more. Addresses are very secured on its own that a person can only watch but no access to the coins in the address. The level of scammers we deal with in this Modern world is alarming and demands extreme carefulness both online and offline. Announcing the amount contained in a wallet as the OP did can even make a scammer more interested in breaking into wallets and will try relentlessly until he succeeds or gets tired of trying.