The most practical approach:
There is a well-known, open-source wrapper called . This tool extracts the VirtualBox installation files and configures them to run from a removable drive.
If you absolutely require a hypervisor that can run without being "installed" on the host machine, consider these alternatives:
VMware requires specific network drivers to function. Unofficial portable versions attempt to bypass driver installation or use generic drivers. This often results in crashes, blue screens of death (BSOD), or the inability to connect the VM to the internet.