imo, sodium hypochlorite is the clear choice.
I just spray them with a hose.
Bleach would be best if you want to sanitize IMO.
1:10 referrers to one part bleach, ten parts water I believe.
Bleach will evaporate and not leave any chemicals behind.
Just rinse it well afterwards, and let it totally dry.
assuming we are talking about real branches and not bio-(ick)vines, i agree with solid snake that bleach is the best way although, imo i would use a 1:4 bleach:water ratio (assuming we are talking about household bleach, industrial bleach is about 3x stronger, household bleach is usually<6%, industrial bleach is usually around 15%).
imo any chemical disinfectant used should be approved for use with food contact surfaces, since chams are subject to drinking from vines, and some feeders like crickets are subject to chewing on vines. bleach is the safest/most readily available chemical sanitizer. bleach is approved by the usda for use with human food contact surfaces. its made mostly from salt water, and reverts back to mostly salt water shortly after being used, so, imo bleach is best/safest/cheapest choice. imo, all those $10 bottles of mite cleaner just a scam, bleach is safer, works better and a $1.39 bottle is enough for at least a year of some serious disinfecting sessions. (should be noted its subject to a gradual decline in potency over time, even when left in the bottle, so imo should be replaced yearly). a simple dedicated spray bottle is usually plenty for a disinfecting session, thats about $0.03 worth lol.
also, if you have branches that are chalky or like to shed pieces of bark, you can blast them off at the car wash and seal them with hot wax. their hot wax solution is almost always a dilute carnuba solution, which is also relatively harmless in small qtys. ( carnuba is often used in food products like chocolate and lip balm/cosmetics. hot waxing can reduce chalky or shedding branches, and if your animal decides to drink off of them , you dont have to be paranoid about what you used to disinfect them with (assuming they are a cham safe plant to begin with). as for bio-vines, the best way to disinfect them, is in an incinerator. jmo
ps dont just spray it on then rinse it off. it needs to partially evaporate in order to oxidize, and it needs to oxidize in order to sanitize, so spray it on , let sit till almost dry, then rinse off (easier to rinse if you dont let it dry completely), and letting it dry completely can leave salt residue. same goes for cages and equip, i always bleach, semi-dry, rinse, hot wax ( i'll admit the hot wax is optional, its just sort of a xantho thing! )