CDs can be cut into any shape as long as it's reasonably balanced and has enough contact points with the disc holder.  For example the "business card" discs are round on two sides and very balanced.  They fit into the smaller disc holder on your CD drive and work well.  On the other hand, some other discs aren't balanced exactly but have enough touch points to keep them in place.

As an example of a disc that doesn't work well there are Digicards™ which are flat on all four sides.  They use four small pushed out points on the disc to hold it in the CD player.  In our experience this is not enough contact to prevent the discs from picking up large amounts of vibration.  Indeed it took us several minutes with many failed attempts to pull a short QT file from one of the discs a company sent us.  That problem hasn't surfaced in the rounded sided CDs.

The following are examples only of shaped CDs.  Custom shaped discs are very possible.  Let us help you with the balancing.