So basically, you don't need to make a new database

Just share the old one.
I don't use wordpress, but I bet all the tables look something like...
wp_data
wp_emails
wp_settings
etc. etc.
When you install threads, (as Giz says) the table prefix can be used to differentiate between scripts

Threads looks like this...
ubbt_ADDRESS_BOOK
ubbt_ADMIN_LOG
ubbt_ADMIN_SEARCHES
ubbt_ANNOUNCEMENTS
etc. etc.

So you just need to enter your database details (you must have had these previously, in order to create the wordpress blog) and threads will do the rest

BACKUP YOUR DATABASE FIRST!