This is an easy project to do. A few years ago I designed my own alarm clock because I wanted all kinds of cool features.
But if I wasn't an engineer, I'd take one of the following approach.
Hire a product development firm. If you have the money this is probably the easiest option.
1. Create some sketches of what I want. Or hire an art student to create some sketches.
2. Define the requirements. Map out exactly what the alarm clock does, how the buttons work, what settings it has, etc...
3. Hire an EE to create the electronics based off the specifications and drawing.
4. Hopefully the EE can also design or outsource the design of the housing. If not, also hire an ME to design the housing.
5. Send design to be manufactured.
If you want to give me details, I'll let you know how much I'd charge to make it so you can get an idea of development cost. Just off the top of my head, I'd say I'd probably charge 80 hours of work at $100 per hour for the electronics, and $40 per hour for the housing (I think I'd need 40-100 hours for the housing, but an ME could probably do it in half that time).