Azure Application Gateway with Service Fabric
Approach 2 is what we are using, We have kept the load balancer and that is routing any request received from the Application Gateway. We found this to be easiest and simplest choice, as this involves minimum changes to be done in Application Gateway.
Your two web api's can run on every node in the VM scale set. The Azure Load Balancer is used to distribute traffic over those nodes. Targeting a single service on a single node will reduce scalability and fault tolerance.
You could use the App Gateway to translate incoming request to different ports on the Load Balancer. (E.g. direct traffic to API 1 @url ~/1/ and API 2 @url ~/2/)
Favor using load balancing rules (using all nodes) over NAT redirections (to single nodes). This way you'll have a performant, reliable system.
Solution 2 would also provide possibly to create VPN connection e.g to manage your cluster. Then no need to expose management endpoint to the public. Internal lb also brings on additional features to utilize in the future.