When is your wood trixie wheel arriving? I think delivery from Amazon is much quicker than from Zooplus although it may cost a little bit more on Amazon. My only thoughts about removing the wheel before the replacement arrives is - your hamster may well go stir crazy snd start bar chewing and pestering to be out (there is nothing worse than the sound of bar chewing).
Totally understand that sleep deprivation is hell. It may be a bit off beat but could you sleep somewhere else for a couple of nights - eg in someone else’s room on a camp bed or on the sofa. Or - ear plugs do work! I had to use them once when working nights and trying to sleep during the day.
There is also the faff of having to paint the truxie wheel delaying things although it literally only takes 10 minutes to paint and a first coat would be dry a few hours later. Under the circumstances I would just do one coat (you can always do another coat in future after wiping the wheel eg).
It is quite stressful I know. I had a wheel break on me and couldn’t get another one for a few days. Hamster going bananas and bar chewing. So I got a 12” flying saucer be t day delivery from Amazon to tide things over till the wheel arrived. Would that be an option?
It was this one
Trixie Running Plastic Disc, 30 cm: Amazon.co.uk: Pet Supplies
It’s not good for long term use - they do better with an upright wheel so they can run properly - but I used it in a playpen afterwards and it’s a good short term wheel substitute. It’s not noisy at all - virtually silent apart from the patter of feet.