In solo piano,it all depends on what type of tune /groove it is, as for the way one would approach or look at playing a particular tune. One wouldn't approach playing "A train" the same as playing "Body and Soul" or ?.
Some tunes would work in using "George Shearing" block chord style.some work better with that Red Garland style.
If you are playing the melody more linear (single note) in the right hand,than it is obvious that the shell voicing alone is not gonna cut it exclusively for solo piano.
Initially,I would keep the two approaches seperate as for the basic two hand fingering though of course you can mix and match them within the tune.
Left hand either the 1,1-5,1-7,1-10th etc. with the remaining notes (chordal voicing) built on the right hand with the melody note on top OR
a linear single note melody occasionaly doubled in the right hand and your shell voicing in the left with that comp chord following.
I find if you keep the approaches seperate it is much easier to preliminarily sight read a fake book chart as for solo piano.
Was that a personal convoluted explanation or what ?.