Thicknessing timber?

I have some very old very good mahogany timber that i've been saving for guitar neck blanks. Some of the planks are over 6 feet long, and a little under 1 inch thick.
I'd like to split it into a 5mm blanks to build a couple of ukes, but i'm not sure how best to achieve it.
Can it be done using a bandsaw an a fence? Or is there a better way?

You didn't say how wide the boards are but find the boards with quartersawn grain. http://en.wikipedia.org/wiki/Quarter_sawing Crosscut the boards into sections slightly longer than the length of the unbent sides and body. Layout and rip the board to rough dimension with as much of the quatersawn section of the board in the sides and top as possible. The back can have some flatsawn grain but quartersawn is much more stable. Avoid the middle or Pith section of the log as this wood is the most unstable. Resaw the pieces in half and half again with the flat side against a large fence or single point resaw guide. 3 teeth per inch, hook tooth blade is what I use.

Alternately you can use a tablesaw with a ripping blade extended to slightly over half the width and resaw the rough cut boards on edge with a tall fence extennsion. Run one side on edge, flip the board, run the other side. You'll waste more wood to the kerf (~ over 1/8" per cut) so you will only get 2 pieces per board.

Please be safe and keep the blood on the inside.

Bandsaw is the tool of choice.