Is there an actually an alternative to using Diffie Hellman in TLS handshake?
This depends on the TLS version you're using. 

In TLS 1.2, keys can be exchanged via RSA, DH (Diffie-Hellman over a Finite Field), ECDH (Diffie-Hellman over an Elliptic Curve), DHE (DH but the key is discarded after use to provide forward-secrecy), ECDHE (ECDH but the key is discarded after use to provide forward secrecy), PSK (Pre-Shared keys), and SRP (Secure Remote Password protocol).

In TLS 1.3 the insecure and overly-complex methods were deprecated, leaving only DHE and ECDHE for key agreement.

Versions of TLS before 1.2 don't have any unconditionally secure cipher options, and should not be used. 

Wikipedia has a nice table, though note that it shows both the key exchange/agreement method and the authentication method in one chart, so there can be multiple rows using a given key exchange/agreement method.