Can I use migration assistant without using wifi?

Yes. In fact WiFi is generally slower than other methods and more prone to errors, say from interference.

I have used Migration Assistant more than a dozen times, all successful and without a hitch. In each case I used a Time Machine backup, except one where I used a "clone" type backup made with a program called SuperDuper. You select the option in Migration Assistant to migrate from an external backup disk, and then connect the backup disk to the computer you want to migrate to. The migration is fast because it proceeds through a cable and will go as fast as the disk can be read from.

Yes, the problem with using Wi-Fi is that it is too slow for transferring this much data reliably. While Wi-Fi will sometimes work correctly, it may not other times. I would never use it for this process. I strongly recommend using a USB cable which should give you a faster transfer without having any corruption of data.