Re-using blog selector control in custom widget designer

I have created a custom widget designer for a custom BlogArchive Widget that I extended the default BlogArchive widget from Sitefinity.

In my custom widget designer, I allow the user to select the blog they want to display the archives for using a standard dropdown field (see screenshot 1).

I'd like to utilize the built in Sitefinity functionality that allows you to select a blog. For example, I'd like my custom widget designer to have the same "select blog" functionality as the default BlogPosts Widget (see screenshot 2), which allows you to search the blogs and select them.

How can I use this blog selector control in my custom widget designer instead of the standard dropdown that I've created?