The admin change form is all automated--sending replies back through the approval emails will not do anything.
We do not want to really be involved in internal club politics--that is one of several reasons we use an automated change form.
With that in mind, I can offer you a few tips. The admin change form for club websites has 3 people that can approve the change: the current admin, the current club president (you), and the email address listed as the club contact in Find A Club (starts w/ kseniiashtoko ... ).
Thus, the key is to have the admin change approved by either whoever is listed as the current club president in your website (you) or the person associated with the email address in the find a club listing for your club. Just be prepared to quickly approve the change after the admin change form is submitted--usually, the emails containing the approval links should be received within ~15 minutes or less of submitting the form, depending on how busy the server is. You have to be prepared that sometimes the approval email gets lands the spam folder--be prepared to look for it.
Therefore, with a little coordination, planning, and quick response to the approval email(s), you should be able to use the form to change the admin to whoever the new admin should be without having to deal with the current admin approver. It can only be 1 registered person / email address; however, you can certainly share the admin password.
You could probably get this done yourself if you are willing to watch your email inbox (for the email containing the approval link) for about 15 mins after submitting the admin change form. (You can put someone else's name and email address in the form.) You can click the following to access the admin change form:
www.toastmastersclubs.org/change/