Simon, your problem is simply you don't know the right dosage.
I believe sodium thiosulfate (anti chlorine)
crystals are the cheapest, fastest, and safest way. You need to calculate how much water you drain by looking at the dimensions of your pond and how low the water level goes down. From there you can at least estimate how much water you drained. Once you figure that out, buy a digital gram scale like this
. Then go to this site
to calculate exactly how much crystals you need to put in. Better to first pour some water in a small container then mix the required crystals to make the solution, then pour it where your tap water is coming in. Also don't turn on a tap water hose directly into your pond full blast in the path of kois swimming lest their gills get burned. Better to put it indirectly somewhere in your filter system like the settlement or vortex chamber. Also if you throw crystals directly into your pond, the koi might accidentally eat them whole.
The only other option I know of are carbon filters. I'll list the pros and cons to better summarize
Pros of Sodium Thiosulfate
1. Dirt cheap. I have a 2400 gallon pond which I do 10% water change every week. I need only 15 grams of crystals each change. A kilo of ST costs only US$ 4.00 where I am. Do the math, that's more than a year's supply.
2. Safe for fish. Chemically deactivates Chlorine and breaks chloramine bonds leaving the ammonia to be taken care of by the filter bacteria.
3. Don't worry about over dosing. If I remember right, you'd need to put in about 100x overdose before you'd kill a fish
Cons of Carbon Filters
1. Expensive by comparison
2. Need to replace it periodically. Especially with big ponds. The biggest problem with it is you don't know when you need to replace it. Its easy to forget.
3. Slow. You can't turn on the water full blast if you're refilling the pond, it has to be slow to moderate flow. Takes a long time for big ponds. In my case, I can't start my filter system unless the main pond is filled or else my sequence pump will be sucking air.
Also take into consideration that 10% tap water is diluted with 90% pond water. So even if there are still some chlorine/chloramine left over, I assume it will react with all the stuff in the 90% and rendered harmless. Chlorine dissipates in a day or so. So I don't believe the kois will be in any kind of danger.
But as with koi kichi folk, if you can afford to do both, why not?
Slow drip from the tap water faucet is also a good alternative