I repair my rosary beads all the time.
If I can’t twist the links with two pairs of needle nose pliers to open them enough to relink them, then I get one of those wire supermarket ties [the kind you use for plastic bags of fruit and veggies] and strip off the paper so all I have is a short piece of very thin wire.
I use a single edge razor blade to trim off the paper.
Then I use the wire to link the two chain ends, and twist them so that the connection is secure. Then I use a pair of small wire cutters to nip off the end.
If a bead breaks, I use epoxy to fabricate a new bead. At most hardware stores or at Home Depot/Lowe’s, they sell a tube about an inch in diameter and three to six inches long and inside is what looks like clay. But it has a core. The outer layer and the core are of two different clay-like materials … the resin is on the outside and the hardener is on the inside. Cut off a thin piece with both the outer layer and the core, mix them up like play dough, so they are all one color and use it to make a bead around the chain. It will harden / cure in 20 minutes.
Use a single edge razor blade to slice off a very small amount of the epoxy putty.
The “brand” I have is “Oatey” Fix-It Stick … All Purpose Bonding Putty
The stuff lasts forever and you can use it for all kinds of household repairs.
Better than duck tape. [Heresy, I know.]
Inside the tube there is an instruction sheet in several languages.