If its throwing it down I will use our Cadac "2-Cook Pro Delux" a two ring stove with griddling platers, in the awning.
Clearly using care its way from the awning surfaces, and with the awning very well ventilated. In just the same way we used a two ring stove for many years in the kitchen section of our Blacks frame tent through the sixties and much of the seventies.
Re monoxide; in the awning as used the stove is every bit as well ventilated as we could ever make the caravan's three burner ring hob, though the van has a CO alarm which has never acted in a threat situation.
Re fat splatters; I have a DIY three faced aluminium sheet shield around the stove. It is better protected than the furnishings of the van abutting that's hob. The Cadac is about a metre from the nearest surface of the awning.
Plus, we do the absolute minimum of fat containing cooking. Typically, I also cover cooking items with old aluminium foil containers, here to retain all round cooking heat, that also serves to contain spits. Pans would normally be used with their lids in place.
If we were into burning food as seems quite common with others, I would not entertain using any cooker other than outside, plus we would also opt out of eating it.