The point is that the module you are seeking is not a CB plugin. Any joomla contact module can work. There are many of these in the extenstions.joomla.org. This is a possible solution as long as you only need it to send to one user for all CB profiles.You only to modify the template a bit perhaps. So any of these might do the trick:
extensions.joomla.org/extensions/extension?searchall=&filter[tags][]=&filter[core_catid]=51&filter[includes]=mod&filter[versions]=&filter[type]=&filter[hasdemo]=&order=&filter[newupdated]=&filter[score]=&filter[favourites]=&dir=DESC&limitstart=0&controller=filter&view=extension&layout=list&Itemid=145&clearorders=0&clearfilters=1