@AM453 is absolutely right, @lightcurtains.
If you can afford a cleaner, and it will make your wife's life easier, whilst she is at the pointy end of new motherhood and recovering from the birth, it is not reasonable of you to let your hang-ups get in the way of what your wife needs. So unless you are willing to shoulder all the cleaning/housework, whilst your wife looks after herself and your new baby, you need to get over yourself and get a cleaner in.
I would have loved to have a cleaner, even just once a week or once a fortnight, when I had my babies - it would have made my life so much easier - and might have helped me cope with post natal depression too (because I wouldn't have been feeling guilty about not having done the housework).
We have cleaners now - they come in once a fortnight, and they are an absolute godsend. Two or three of them come, they are in the house for 2 hours or less, and in that time they completely clean either downstairs or upstairs, and the house looks lovely afterwards. We have them because I have long covid, which has severely reduced the amount that I can do around the house, and whilst dh is only working part time, from home, he cannot cope with everything that needs doing. Our cleaners used to come once a month, but we have put it up to once a fortnight, because he needs that help.
I don't feel entirely comfortable, having the cleaners in - even though they are lovely, friendly ladies, and entirely unjudgemental - but that is my hang-up, and it would be very unreasonable of me to refuse to put up with some minor discomfort, in order to help dh.