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First of all, you do not need to remove the lower interior skins in order to work on the bellypan of a 70's vintage trailer. The skins do not wrap up over the C-channels like in earlier models. The entire bellypan can be removed from the outside without touching the interior skins.
Now in response to your question about riveting the interior skins in place, the argument for using aluminum mandrel pop rivets is the following:
1) They aren't going to get loose as you travel down the road (like a sheet metal screw might).
2) They provide a "weak link" so to speak. That is to say, if you get a vibration, or movement in the structure that might cause the pop rivet to shear, you would rather the rivet shear than to have the skin tear. If you put a stainless steel screw in there, the skin will tear around it.
3) Installing pop rivets is easy. You can use a $5 manually operated tool, and gain some forearm strength, or buy a ~$30 pneumatic tool from harbor Freight, which will get the job done and make it easy.
4) Finally, you are very likely never going to open up those panels again anyway. Hopefully the repair work you are doing will last for decades and not require intervention anytime soon. Besides, once you have installed all that cabinetry, bathroom, galley, gauchos, etc., those lower skins won't be easily accessible anymore anyway.