Is it ok to wear trainers?

I will be visiting Japan for the first time. I have problem feet that I cannot wear most slip-on shoes (except one pair of boots I have). I will be doing lots of walking, visiting temples and castles. I am aware that many public places require you to remove shoes, thus slip-on shoes seem to be often advised. I normally wear special trainers and would not mind taking them off and putting them back on many times. Is it OK to wear them? They are black.

That will be fine. I have always worn trainers or similar on visits to Japan.

No problem unless you take off the shoes as you go inside temples/shrines. You must wear socks too. Stepping inside temples/shrine where holy places with bare foot is very rude manner.

Many thanks to you both for the advice. It is very reassuring.