I'd start with trying to find aarch64 container images. Search "image name aarch64". If the source is available you could also build the image yourself, but I've never found software I wanted to use badly enough to do that. If you're lucky someone already did it for you, but these images often aren't kept up to date. Do the community a favor and drop the owner an issue asking for aarch64 builds if nothing else.

You probably want to use qemu for that. You might be able to find some tutorials on setting up a chroot in the context of people doing the opposite for running or compiling stuff for their arm based pi or similar systems on their PCs.

The way to do it as seamlessly as possible is to not use docker and instead use a distro that has first-class aarch64 support. I like my free Oracle VM and haven't had any issues with it whatsoever (besides having to deal with the atrocious web control panel when first setting it up).