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Hello. My hamsters have those too

With all wood hamster houses, most people paint them with plastikote water based enamel paint. It's classed as pet-safe and been used for many years by hamster owners. It makes the wood wipe clean. I only paint the inside of the houses and sometimes the top of the roof but not always

Some people paint the whole thing, depending on the type of house. The reason I only paint the inside is to make sure the lid still fits properly - a layer of paint could make it too tight to fit. I think painting the inside is sufficient. But with the Happy Henry Homes ones, it's best to paint after you've assembled it - they come like pieces of a jigsaw you fit together. If you paint the pieces individually then they won't fit together! So best to paint inside after it's assembled. This does mean it won't come apart again, as painting the inside kind of sticks the pieces together, but I don't see that as an issue! If anything it makes it more stable so bits don't slide out of place.
Painting the top of the roof is optional - sometimes I do it, but most of my syrians have never pee'd on house roofs (I did have one that did) but I also put a granite slate on it under a water bottle.
Plastikote is about £5 a pot. It's a very small pot but it goes a long way and you probably wouldn't even use half a pot - it's quite thin. It needs two coats usually to be wipe clean. It also comes in various colours! I tend to use the clear one but have sometimes used the flat white one or harbour blue which is quite nice for a roof.
Clear plastikote
Flat white plastikote
Harbour blue plastikote