No, there isn't - your two choices in the connection string are Integrated Authentication (the current Windows user) and SQL authentication.
If I understand you correctly, what you're trying to do it log in to the SQL Server as a different Windows user. You can look at either impersonating a user (though this would have to be a separate process, not your main application), or you can look into something like Database Roles:
MSDN Article
UPDATE: Since you've stated that you're in a workgroup (I assume both the client and server are), then this blog post seems to say that as long as the username and password you're using exactly match a user on the server, you should be okay. Not sure if this is a possibility, but worth consider. Also, if either computer is on a domain, the bet is off - in that case, you'll have to impersonate to make this happen.