UUID vs Compound Key

Each "site" has a unique alphanumeric identifier. I use this to uniquely identify the "site" in the centralised database by making a compound key out of each table's primary key plus the identifier:

For example:

SiteUserTable

sitekey CHAR(16),
id AUTO INCREMENT,
firstname VARCHAR(255),
surname VARCHAR(255),
timestamp TIMESTAMP,
etc..
PRIMARY KEY sitekey, id;

Please note this is not the actual table definition - it's for illustration only. Also, there are *many* tables using this composite key.

So basically, I end up with data like this on the centralised database:

SITE_1, 1, Fred, Flintstone
SITE_1, 2, Wilma, Flintstone
SITE_2, 1, Homer, Simpson
SITE_3, 1, Foo, Bar
SITE_1, 3, Barny, Rubble

Now, the only downside I've found with this is that because I'm using a compound key, it makes me queries more complicated. This is fine, but I'm wondering if I'm missing a trick.

If I use GUID's then I can just use that as the primary key, and I won't have to constantly use the sitekey.

However, I'm then storing a much larger primary key and I've read this can introduce performance problems amongst other things.