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most "modern" /out/ wool stuff (smartwool, icebreaker et al.) is machine washable on 30° and with a good wool detergent (get a special one for wool, really helps). From my experience, that works well with T-shirts, underpants and socks. However I had a few pullovers shrink, even though I was washing them in the 30° wool cicle. So I now hand-wash them.
But really, it's not big hassle. If you have a few to cycle through and let them air out in between wears and wear underwear below, you can easily go a full trip (when sweating a lot and only having 1-2 days between wears) or even a few days of constant 24-7 wear without totally reeking or even w few months, if you only wear them the occasional weekend or as normal wear casually. I.e. I have a lot of fashion/business casual merino and cashmere sweaters which I only wear with a T-shirt or dress shirt below, and I wash them on average twice a year. Once at the end of winter, when they're starting to spend most of their days in the cupboard and once in early winter, to wash out the few summer wears and the first month or so of intense wear.
Incidentally, I use quite a few of my icebreakers in the office and have also worn my cheaper fashion pieces climbing. So if you wanna get some cheap sweaters, also check out normal departent stores when they're having sales.