A normal Club would be sufficent. The tune is a nice example of what I wrote in another thread: It twiddles around with the C-note in the melody. It switches colour, because the underlying chords alternate between tonic and dominant. That's what the Gleichton is made for.
The "black notes" are just embellishment, they don't belong to the core melody. You can play them, if your box has them. If not, just leave them out. It is played in F major. Your accordion is in C major, if I remember correctly, so you can't play it at the same pitch, but have to transpose. You could try to start with something like this:
X:1
T:Hillbilly Polka
M:2/4
L:1/8
Q:1/4=100
K:C
"C" G/G/G/A/ G/G/G/A/ | GE C z/G/ |Gc BA |"G" GF F z/G/ |
GG AB | AG F z/G/ | GG AB |"C" cB AG :|
(I would add right hand chords, not just the melody.)
Where the chord switches from "C" to "G", you have a problem, because you have the "G" chord on pull, whereas on the right hand side you have to play a push note (G). (I insertet some F notes, where in the original they should be G notes. But at least F is playable on the pull, so you can play the right basses. Don't know if it sounds good.) You have to experiment a bit.