Launch the editor directly in your browser (Chrome is recommended).
Fusion 360 updates nearly every month; a portable version will quickly become incompatible with your cloud files. The Official Alternative: Fusion 360 in a Web Browser fusion 360 portable download install
You cannot run Fusion 360 from a USB drive on a different computer. But you can carry your with you. Launch the editor directly in your browser (Chrome
If you absolutely cannot install any software on the host computer (e.g., a locked-down public library PC), there is one legitimate workaround: a locked-down public library PC)