DSNs are hard coded, so you would have to setup a local DSN on each machine with that username and password for each user instead of your "sa" user account. You can also remove the user/password from the DSN as well, which will force it to be connected via the credentials stored in the filemaker external data source.
In filemaker, the username and password fields for connecting to external data sources are calculations, so you could do a calculation there like:
Get(AccountName) = "User1" ; "User1 SQL account" ;
Get(AccountName) = "User2" ; "User2 SQL account" ;
What might be a better idea would be just adding columns to the SQL tables for creation/modification user, and setting those from filemaker. Rather than relying on the SQL log.