Since you already hava java applets, looks like developing it in Java Swing is a no brainer. Bundle JVM with your application. Yes, it will take ~50 megs in size, but:
1. It is cross-platform (yes, to the extent) but much better than anything else out there.
2. Pluggable LaF.
3. Utilize your java skills and knoweldge.
4. Potentially - easy start on Android.