If you'd like your affiliates to see and use only your customized panel themes, you can disable any theme, or alternatively remove all the buttons/menu items leading to the Themes/Theme settings section from the affiliate panel.
To remove the elements, as a merchant navigate to Configuration > Design > Affiliate panel theme and edit your active theme (create a copy if needed).
In the theme editor, search for and access the system_menu.tpl file, and delete in it the widget with ID "PanelSettings" {widget id="PanelSettings" class="hide_if_empty"}.
Subsequently, search for and access the myprofile.tpl file, and delete in it the widget with ID "Themes" {widget id="Themes"} as well, and optionally add the following code below the <!-- myprofile --> part to align the rest of the items in the My profile section properly:
<style>
.flexPanel {
justify-content: normal;
}
</style>
Do not forget to set your customized theme as the default for the affiliate panel and apply it for all existing users.