I have a modern .54 cal Euroarms flintlock
I have fired it about 10 times now using .530 ball. Loading it with pre-lubed CVA patches (.50 to .58 cal) seems tight.
I also have two boxes of .535 balls that are untried yet.
Question: Can the larger lead balls be fired without patches
Take a trip off to Fabricland, take a set of calipers with you, stand in the middle of the store looking helpless until someone takes pity on you, tell em you want the tightest weave all natural (cotton) fabric they have, preferably on sale.
You'll probably find a few different thicknesses, You should be able to get a square metre of something for $15-$20(ish). Stuff that is ironed smooth (like a suit) loads really well. Buy a couple different thicknesses - or more. You probably won't find anything less than 0.010" anyway. but if some of it does not work out - you can use it for cleaning patches
Cut it into strips, roll it up and let soak in your favourite lube - I stuck mine in a little tub with lube and let it sit in the hot car for a few days.
Cut as needed - you get a perfect patch every time for less than half the cost of buying them AND you don't have to buy a bunch of different sized pre cuts!

(there are other downsides to pre cut patches as well...)
consulting the internet, sounds like those patches are 0.015" thick - making your total load 0.560" diameter, if that "seems tight" an 0.010" patch would probably make loading much easier. Though a smaller ball and thicker patch would probably be better for accuracy. (easier to load, better engagement of the rifling and less tendency for the patch to tear)
But to answer the actual question " Can the larger lead balls be fired without patches"
Sure, why not - but you won't have any accuracy - the patches are there to engage the rifling, i.e. without one, your ball probably won't spin, without a patch you get too much blow by and loss of pressure.
Hang onto them (the larger balls) maybe down the road you will find a gun that likes them, sell them, melt em down and cast different sized balls... whatever - it's not like a box of balls is expensive.