The clients need to be able to access the Internet in some manner. Are the clients able to browse the Internet without Squid? Actually a better question, can the clients all ping addresses on the Internet, such as www.google.com?
If the clients can access the Internet, then you just configure their e-mail clients to talk directly to your ISP's SMTP and POP server.
If the clients cannot access the Internet, then you need to provide access some how, such as through a dual-homed box that does ip-masquerade.