I know your pain.
Where I live we have frequent tornado warnings and one year a tornado completely destroyed our highschool to the ground and 9 kids were killed..
Very sobering.
And scary..
In the event of a actual warning with sirens going off, just grab him and worry about the rest later. Put him in a tub at first, less stress then holding him. If temps really start to go down, you can always warm him on your body. But always do the least stressful thing while still doing the necessary thing.
Have a pillow case ready. This way you can keep him in a dark and enclosed space and he won't move around much if you have to hold him. Less danger of him stressing.