Yes fifths on both sides is possible.

There are not really any tunings to refer to because there are no 'official', or even any popular, dual fifths tunings, even for other brands of tapguitar.
(The Touch Guitars 10 string tuning is not pure fifths on the melody side, it also contains a minor third.)
You just have to design a tuning according to your needs.

A 10 string tuning i thought of, which covers the entire pitch range of available Stick strings (Bb0 to D4) is:
Bass (low to high): BbFCGD (Bb0 to D3)
Melody (low to high): BbFCGD (Bb1 to D4)
The two sides are offset by an octave.

Since you wouldn't be downtuning I think you'd be able to use the same gauges as your 10 string tuning- I don't believe different gauges are required between 34" and 36" scale instruments for the same tuning.

I will design this tuning for you now

10 string Classic tuning has the melody side tuned as high as possible, therefore the top string is D4, the highest possible pitch on a 34" scale (or X fret on 36" scale) instrument.

So for your requested tuning, it seems appropriate for the melody side to choose 5 strings in fifths tuned as high as possible, therefore the top string is D4.
Adding the Classic bass side tuning, the result is:

Bass (low to high): CGDAE (C1 to E3)
Melody (low to high): BbFCGD (Bb1 to D4)

I consider this the 'dual fifths' equivalent of 10 string Classic tuning.
The offset between the sides is 10 semitones.