When I bought my Zephyr, I was using Phonak’s with a battery, not a rechargeable, so that was never an issue. The cycle is 8 hours.
When I got my (short-lived) rechargeable Signia’s which has a non-dehydrating charger, the Audi suggested I use my Zephyr on the week-end or whenever I could fit in the separate cycle once a week. A 3 + 8 hour cycle was inconvenient to say the least. Worst than that though, she did not know, and neither did I until just yesterday when I checked the manufacturer’s web site (prompted by your query, thx!), that the Zephyr model produces too much heat for a rechargeable; it can damage the battery. The same company produces a unit using UV heat (called DryBoost, ~$115) which is safe; you actually place your standard charger inside this unit so the cycles run in parallel but it is still 6 hours. There are other UV drying units such as the PerfectDry Lux (~$60) which has a <1 hour cycle, making for a 3 + 1 hour total cycle.
After switching to Oticon rechargeables, I had the same challenge as you. My Zephyr is now useless. Fortunately Oticon offers a dehydrating “smart charger” for its rechargeables, so that is my solution.
For your KS10’s, good and bad news. The bad - afaict from the literature - is that the Costco charger does not provide dehydration nor does it allow for adding a desiccant, so if you want dehydration that means buying a unit like the DryBoost or the PerfectDry LUX. The good news though is that the Phonak counterpart charger (~$135) does have a compartment for adding a desiccant, and it is highly likely to work fine with your KS10’s (but of course you would need to verify that, and pay a bit more).
If audiologists like Cliff Olson are to be believed, this is not a trivial issue. Apparently moisture getting into HA’s electronics is one of the more frequent causes for repair.
Good luck.