Hiya. This is an older post but I`ve kept mice for a good while so can give you some pointers. Males do indeed stink but so do female mice in a `lesser` way, but you do get used to the scent (can`t say your family members or visitors will though!) Depends if the cage is situated in your own room space and away from the main living areas.
What I did when cleaning my small groups or single males, was to spot clean daily. Males spot urine a lot and they like their own `smell` so the more you remove, the more they will scent. I never used pet cleaning sprays either as mice suffer from chest infections derived from the bacteria mycoplasma. Much as rats do. So you want to be using paper based ONLY bedding and remove the areas that look or feel damp and replenish daily with a few handfuls of fresh bedding/substrate.
The cage base can indeed be washed out every few months if and when required outside with a spray or just washing up liquid and rinsed and dried well. But I rarely needed to. I wiped around the cage using kitchen towel and warm water only. Wash accessories though like the wheel (as this can build up with urine as the mice run on it) and helps to reduce the smell.
The mice were always in the cage when I done all this and they liked helping out by getting in the way! But that`s the fun part! Taking your time and moving the substrate to one end and then wiping the base and then moving it back again with a few fresh handfuls and mixing it in. Did exactly the same with all the hamsters I had and it also meant I wasn`t throwing out what I considered to be perfectly good bedding. The nesting areas rarely get soiled or smelly, but worth puting your hand in now and then and having a `sniff` just to be sure. Nothing better than getting your nose down into it!
The mice/hamsters always (I felt) appreciated this non-invasive cleaning and as the owner, it means you can interact with your little ones while also (and this is important) that the cage base is not high off the floor if you tend to have a hamster or mice that like hopping over the edge! NEVER leave the cage lid off if you leave the room either, which is just common sense. This also reduces any stress on small animals who feel their home is being invaded! Less is more in my view and I know many hamster, rat, mouse and gerbil owners may not agree. But I also kept gerbils too and they had large glass tanks and I practiced the very same with them. Miss keeping them sorely but my circumstances changed in a way that doesn`t allow me the quality time I used to have so I haven`t had any small pets since I lost my last dwarf hamster. Hope anyone reading finds this useful though. x