If find is available, try:
find / -type f -exec grep -rHinF --colour=always -e "aa:aa:aa:aa" {} +
This only applies to regular files so it will skip block and character devices. See man find.
You probably want to skip directories like /proc or /sys; as Stephane Chazelas points out in the comments, some files in there will block (remain open, hanging the search) when you read them. To do this, you could try the -xdev aka. -mount directive, presuming the rest of your filesystem is on one device. If the -fstype directive works for you, that would be better (unfortunately it does not work for me on linux).
IMO, rather than fiddling with this, you should just repeat the process for whichever toplevel directories you really want to search, rather than trying to do it all in one go (in which case you may not need find...)