If the prongs spacing is standard then It does look like an extension cord will fit. Easy enough to try before you connect the other end to the wall outlet.
The tape recorder doesn't need a heavy cord. Anything you use will be fine.
If the machine hasn't been powered up and used for a while be prepared for it not to work. There are a lot of rubber bits that are perished, capacitors and resistors no longer meeting their specs and maybe tubes that need replacement. It would be a project with a long learning curve.