The sharp turn-on current transients generated by the the triacs causes EMI radiation from the power lines. This can be readily heard from an AM radio if you use typical light dimmers, which are not well EMI suppressed.
The purpose of the chokes is to slow the speed of the transients, reducing the high frequency content, and reducing the EMI. Putting the circuitry in a shield will have little effect on the EMI since it's mostly coming from the power lines.
As you noted, high current inductors in the 100µH range are not readily available.
Here are some choices:
1. Leave out the choke and live with the EMI.
2. Wind you own choke
3. Have a magnetic manufacturer make a custom one.
4. Try an EMI filter I've seen on Ebay such as **broken link removed**