I've been appliqué get for a dog"''s age (that's a really long time!) and have never used a hoop - and have never seen any other appliquér use one either. I think that could have a great possibility of stretching fabrics. Anyway, for me I need to use a flat board on my lap - it's a perfect resting place for my left hand and allows me to fold up the piece so I can get to the appliqué and sew with my right. Sort of almost keeping the block flat but not quite. I have many friends who can just hold up their block and appliqué that way - just cannot do it. I've never had a problem with things not flat, but if you're doing needle turn appliqué the motif can get slightly poofy if it's on the large side and/or is not basted to the background well enough. With needle turn you are always just slightly pushing - very slightly - and if you haven't pinned or used some other basting it can really get pushed out of shape.
I could ramble on and on and on about hand appliqué - but I won't - yet☺️
Sandy in Mooresville, NC