So if I get it right, you want to represent the same data using different units. I can see why plotyy is not the right tool.
You could use a second transparent set of axes.
If h is the handle to your axes, (the one for the left scale),
p = get(h,'position'); % gets the axes position
a = axis(h); % gets the axis limits
h2 = axes('position',p,'color','none'); % draws another axes with transparent background over h.
axis(a); % sets the same limits as in h
hold on;
then you need to get rid of the duplicate stuff. It's probably best to keep only the righ y axis
box off
set(h2,'Xtick',[],'YAxisLocation','right');
Next you need to set the same ticks on the left and right axis
set(h2,'Ytick',get(h,'Ytick'));
Finally, you take care of the new unit
set(h2,'YtickLabel',ytl);
where ytl is a vector containing the appropriate values in the other unit of measure. This should work
set(h2,'YtickLabel',abs(get(h,'YTickLabel'))/0.01*0.0349);
