It will work, and Oli's suggestion of a capacitor is a good one. I'd point out a couple more things:
You don't have any capacitor to block any DC offset on the input. This is fine, if you are going directly to your microphone and you know there won't be any. However, if this is going to a connector on the box, you never know what people will plug in there, and it may work fine, until it doesn't, and your amplifier is fried. It's probably best to go for a non-polarized type here, since you don't know what people will plug into it.
Another issue: "Contact microphone" usually means a piezoelectric microphone. These are different from most other microphone types in that they have a very high output impedance, on the order of \$10M\Omega\$. The input impedance of your amplifier is an order of magnitude less, which will result in significant attenuation of the signal and alter the frequency response of the microphone-amplifier system. It will work, but it may not sound good. This is of course, subjective and depending on the timbre you desire.
The solution is buffering, converting a high impedance output into a low impedance output, or equivalently, amplifying the current. An op-amp can do this in a circuit called a voltage follower:
Put this between your microphone and the input of the circuit you already have (on the microphone's side of the cable, if you can), and your amplifier's input impedance will be that of whatever op-amp you use, without otherwise changing the operation of your circuit. Oddly, I don't see an input impedance listed in the LM833N datasheet, but since it has a BJT input stage, it's probably some megaohms. This is "high", but not higher than the piezo. You'd want to look for an op-amp with a MOSFET input stage with a very high input impedance: TL072 is a common such type with the datasheet listing input impedance at \$10T\Omega\$.