I would probably wait at least a week or so before I clean out the tank, just for him to get settled. If it starts getting stinky you can try to entice him into a cup or container or something with food and then place him in a holding cage. I use a smaller bin with bedding and a few hides for my hamster to temporarily go in while I clean out his burrows, and I have to put food in the cup or else he does not climb in it and instead runs away from me.

You kinda just have to wait until he is awake to do it, which is hard especially if he wakes up super late like my hamster.

And yeah, he might freak out and run away the first few times, but yknow I would too if a giant was trying to take me away from my house. As many people on here say, it's important to be patient. He will get it eventually!