Put the cannon ball in a bucket and cover with fresh water. Go ahead and fill the bucket all the way, the more water the better. A five gallon bucket is perfect.
If you let the ball dry out it's going to crack and fall to pieces. More details on restoration below.
Please do the same thing with the pieces of your disk but use a separate bucket.
Your cannon ball is, most likely, made of iron. Submerged in soil, or salt water, iron absorbs minerals from the surrounding medium. An iron item will remain intact while it remains in the soil or salt water. If you remove it, and let it dry out, the piece will either crumble or fall to pieces.
Soaking the item in fresh water allows the minerals (salt is what we're dealing with) to be leached out of the item, over time. After soaking for a long period, the item can be removed from the water, allowed to dry (the slower the better) and will remain intact.
The appropriate time for soaking your cannon ball should be a minimum of three months. Six months is better. The water should be changed weekly. Keep the bucket where it's easily accessible so you can stir the water with a stick every couple days. This will break up the halo of minerals which has leached from the iron and circulate the water for better dissipation.
Bigger iron items take much more time.
If you have a creek or river nearby, and you think you could put the cannon ball in it and not have it stolen or washed down stream, that would be even better. Constant water circulation like this is great and you don't have to monitor a bucket. A friend of mine did this with an iron cannon he found. He left it submerged in a creek for about a year and it was nicely stabilized when it dried.
Your metal disk. What shape are the pieces? Are they wedge shaped? If they are you may have found a silver bullion disk. Silver wedges from bullion disks were recovered from the wrecks of the 1715 fleet off of Florida. It's possible you found one and the wedges became cemented together by mineralization after being submerged for hundreds of years.
You may have disturbed the very weak corrosion bonding when you handled it which caused it to fall apart.
If that's the case, you haven't done any harm. But soaking the pieces in fresh water will soften up encrustation or other gunk on them and help stabilize the surface of the silver.
Please post pics of the pieces of your disk if they are even remotely uniform looking. I'm really hoping you found a Spanish silver disk.
For future finds, when you're unsure about what they are or what they're made of, try not to be impatient about cleaning them. The best thing you can do is play it save and, as soon as possible, submerge an item in clean, fresh water to stabilize it.......take a couple pics first though so you can post them.
If you have questions or want more info please ask. I'll look up some sites for artifact restoration and post links.
I've included a picture of a silver bullion wedge from the 1715 fleet.
I consider it my best find since getting into the hobby again this year. Just found another gold ring, this time with diamonds but I like the cannonball the best