Without going to a chromatic, you have a few options.

1. The easiest answer is either picking up a Lee Oskar Melody Maker or a Hohner "Country Tuned" Special 20. These specially tuned diatonics have the "F#" already installed on hole 5 draw. If you want the "F" you would need to bend the hole 5 draw down a half-step (it bends a lot like the hole 4 draw bend).
http://www.harmonicastore.com/harm_tuning.shtml

2. If your bending is pretty slick on hole 2 draw, you can bend the 2 draw down only a half-step to get the "F#". Yes, you do have to finish your melody down an octave on the "G" on 2 draw, but in most cases, it sounds fine.

3. Overblows. This is the toughest solution and the one I recommend the least. You would need to be able to overblow on hole 5 blow (E) to get an "F#". This is one of the hardest overblows to accomplish and aside from being difficult to do, it's very tough to play it in tune and also to have it sound "sweet". Overblows work best only on certain types of diatonics and usually need to have the gaps adjusted to increase the ease of overblowing. The standard recommended harmonica is the Hohner Golden Melody. Some overblow posts:
Overblows and Overdraws-
http://www.harmonicalessons.com/members/dcforum/DCForumID2/277.html#1
http://www.harmonicalessons.com/members/dcforum/DCForumID2/267.html#3
http://www.harmonicalessons.com/members/dcforum/DCForumID2/267.html#1
http://www.harmonicalessons.com/members/dcforum/DCForumID4/19.html#1

--
Play on,
Dave Gage

Hear Dave Play:
http://www.myspace.com/davegageband
http://www.myspace.com/harmonicastore