You could do this thing, but think about it: It would make no sense. If the verifying key is part of the package, then _any_ package can supply a key, and the verification means nothing. You, as the user, have to decide you trust a key. That's how public key cryptography works. And you haven't had to install a key before because you've either been installing unsigned packaged, or you've been installing packages from the distribution itself (which comes pre-seeded with the official distribiution keys).

So no - it's not a workaround. It's how public key cryptography in general (and package signing in particular) works.
And no - the key can't be part of the package - that would make the package signature meaningless.

When I run "sudo apt-get update", the following error appears:

Ign:21 http://ppa.launchpad.net/upubuntu-com/ppa/ubuntu xenial/main DEP-11 64x64 Icons
Reading package lists... Done
W: The repository 'http://ppa.launchpad.net/upubuntu-com/ppa/ubuntu xenial Release' does not have a Release file.
N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use.
N: See apt-secure(8) manpage for repository creation and user configuration details.
W: https://download.01.org/gfx/ubuntu/16.04/main/dists/xenial/InRelease: Signature by key 09D6EF97BFB38E916EF060E756A3DEF863961D39 uses weak digest algorithm (SHA1)
E: Failed to fetch http://ppa.launchpad.net/upubuntu-com/ppa/ubuntu/dists/xenial/main/binar...  404  Not Found
E: Some index files failed to download. They have been ignored, or old ones used instead.
 

Same error as I get when I run the packge tool. There is a huge problem here with your key, nothing else so far. It prevents us from moving forward.