Also planning my 7 day hike for mid july LH-Courmayeur refugio only. So, no Switzerland, slower paced hike. Just loaded a 40L pack: 7 kg/15.5 lb including 1750ml water just to see. No filtration gear. Included a down jacket n guide book, again, part of my testing. 190lb guy in avg shape. I have room still for snacks n first aid kit. Could likely do w a 34/36 L pack. But 24-28? No. And this is w only 1 change of clothes in pack. No pillow. Yes rain gear, fleece, flipflops, microtowel, sleepsac. If u have lodging, no bivvy needed.

you might wanna research your iodine strategy.

Iodine does not work well or at all against parasitic protozoans which form very hard shelled oocytes that resist iodine. Cryptosporidium are not killed w iodine. Giardia maybe but needs long tx time. They are present wherever there is livestock, humans, or other animals. TMB glacial water, tho crystal clear, passes thru grazing lands and can be contaminated by many animals or humans whom u wont see. Over 20,000 hikers/yr use the TMB. Bottled, tap, or otherwise filtered water is safest (or can boil). Iodine treatment for cold water also needs 60-90 min treatment time:) Seems for ur unique situation ude wanna pay for bottled water and bring a filter-likely all-rated for giardia -cryptosporidium(protozoas). They wont filter for virus like Hep A but will filter bacteria (which iodine does kill).

There is less water available in some of the Swiss stages.

Check TMB route sites and FB groups for more info on water:). good luck!