Wool isn't as fragile as people think. You do need to treat it with some care, but it won't felt unless you subject it to heat AND moisture AND agitation. If you don't rub it or wring it, you should be fine. Sudden changes in temperature aren't good, either, so use lukewarm water for both washing and rinsing.
After you've given the sweater its soak, lift it with both hands and squeeze out as much water as you can. You can press it against the side of the sink or tub to get out more water. (Remember: don't rub or wring.)
Have a bunch of thick towels ready. Lay the sweater on one of the towels and roll it up to get out even more water.
Lay two more towels on a bed or clean carpet and spread the sweater out on them, front side up. Pat it gently into shape and let it dry. To speed up drying, you can run a fan in its direction, but nothing that emits hot air. When it's half dry, you can flip it onto dry towels to let the back dry. Or you can buy a mesh drying rack that lies across the bathtub and really cuts drying time.
This sounds complicated, but the whole thing should only take 10 to 15 minutes, and it's not an unpleasant process.
When you run out of the lavender wool wash, you can substitute mild shampoo or a dishwashing detergent like Dawn. Best of all is a specialized wool wash such as Eucalan, which may be what the shop gave you. Shampoo and detergent need to be rinsed out; Eucalan doesn't.
Wool can go a surprisingly long time between washings, especially if you don't wear it next to your skin; it doesn't seem to attract dirt the way other fibers do. But don't let it get really filthy, because dirt and sweat can deteriorate the fibers and make it hard to get clean.