How to add a custom html codesnippet to one menu item

This may be a little bit delicate.

For a customer I have to add a div with a certain id to a menu which then gets filled by a third party javascript application with a submenu for this one primary menubutton called "Shop"

I want to have a normal menu, referencing pages from wordpress, except when hovering over the "Shop" Menuitem, which should just display the div which then gets populated.

I hope it is somewhat clear what I mean, please tell me if I should elaborate further.

Thanks for the awesome Theme by the way :)