How do you restore (or check) only the extended properties in a MS SQL Server .Bak file?
There's really no other way that I can think of than restoring the database.  The best option would be to have versioning stored elsewhere so that you don't have to go through all this trouble just to get a version number.

What you could do is have a little configuration file and a small application that performs the backups for you, and stores a key/value pair of filename/version.  That way you will have a reference as to what backup file is for which database version.  An easy application to write and it would save you a ton of time with restoring/querying just to find out this bit of data.