This functionality was a available in Click Once due to it being a Microsoft Windows functionality that existed.  The Web shell version is not capable of using Microsoft functionality such as this and rely on the specific browser's shortcuts being used.  We can use CTRL+F to Find text, but there's no out of the box Find and Replace functionality that exists in web browsers.  With this in mind you may need to use an Addon or extension.

Firefox utilizes Addons that can be installed to complete this type of functionality:
Chrome find/replace extension:

Current short key menus: