Don't think they are likely to choke. We had a rotovirus in the house last year, we were all sick on and off for about 10 weeks (me and mrslister and little listers aged 3 and 14 months)
It was hell, but the best thing was layers of sheets with towels between them on the bed/cot so you can just peel off layers when needed.
We had our little girl in bed with us at the end, we moved down the bed and had her between the pillows surrounded by towels.
We woke everytime she vomited and got really good at pointing her so she didn't get us or her clothes. Just peeled a layer of towels off and chucked them in the garden to hose down the next day!
Our 3 year old got really good at waking and hitting his bedside bucket. We bought him a special bucket and he covered it in stickers. Had it in the car and everything.
Worst 2 months of my life.
Good luck, remember when you're at the end of your tether at 315am that they WILL stop one day… 😉