Sounds like a good plan, though you don't have to do anything to the banjo itself besides remove the 5th string. One of the two styles of 4-string banjos in dixieland is plectrum, which is the same length neck, and tuned essentially like standard C-tuning on a 5 string (as in Home Sweet Home or Farewell Blues): C G B D. So the chording is no different than the 5 string in C tuning.
The other style of 4 string banjo (and it's a more common style) is called tenor and has a shorter neck and a different tuning. You could go ahead and put a tenor neck on your old banjo, and work on tenor that way. But it would be a lot simpler to just use your existing banjo in plectrum tuning, and learn the strumming and flatpicking work that plectrum players do. It's quite similar in sound to tenor playing, and the way it's played (sound-wise and right hand technique-wise) is pretty much the same. If at some point you decide actually learn tenor, you can then learn the chords that go with its different tuning (the pitch intervals of the strings are the same as on a mandolin and so the chord shapes are like mandolin chords, but since the individual string pitches of the tenor and mando tunings are different, the same positions are not the same chords.)
If you do this, you’ll be one of the very few players who learn how to play both types of banjo, 4 or 5 string.
I like Dixieland too, and have sat in with Dixieland bands over the years, just using my 5 string in G tuning. I leave my finger picks on, and mostly using my ring fingernail for "down" and the index pick for "up". When it comes to soloing, I just do that as well as I can Scruggs style, and then the big problems is contending with their typical keys like E-flat and B-flat and such.
My affection for Dixieland is part of why I started Flexigrass (formerly The Live Five), back in 92. I still love playing with that combination of instruments, and I blend my favorite aspects of bluegrass and Dixieland (and other sounds) into the band's sound. It's fun!
Have a great time with your picking, and write when you get your new banjo!