A transformer or small smps would be a more sensible replacement because:
1. 200mA is a lot of wasted power - you are pulling a whole 200mA from the mains supply to feed a <1W circuit
2. A 2.2uF X1 rated capacitor (yes, it does need to be X1 rated for safety, you won't find anything in SMD) is going to be large and potentially expensive.
3. A transformer or small SMPS is likely to be smaller.
4. Isolation from the mains supply is always preferable.
Capacitive droppers are certainly widely used, but for lower current supplies, usually at higher voltages so the efficiency is much better that you have here.