First, I'd like to thank both of you, Gérald and Mediavets. I've found our advices very interesting.
But now my problem has change !
I found that making a partial pano into a fake sphere reduce the quality of the final result. My pano has less resolution, I come faster to 100% and my purpose is to give the best viewable quality to my pictures.
I understand it's an APG issue I have, maybe I should change the place of this topic ?
PTP doesn't support HTML5 multi-resolution output for pano images which use a spherical projection but have a panoFOV of less than 360x180.
You can try forcing a 360x180 panoFOV when stitching your pano and then using the crop tool in the Hotspot editor in PTP 2.0.
But it may not work well, because it will generate a lot of unused tiles.
Try it and see.