AWSALB and AWSALBCORS are 3rd party cookies in web

As you know, ALB supports stickiness with cookie and the cookie could be either ALB generated or Web App generated. If it's not possible to use non of these cookie in your environment, you can think of using NLB instead of ALB. NLB is not for application load balancer and is working at layer 4. But NLB can distribute HTTP traffic and you can use stickiness with source ip address. The other thing you should consider is that Health Check of NLB is not application layer but tcp layer so NLB can't check the health of target group at application layer. If you're OK with source IP stickiness and health check method of NLB is OK to use, you can try to use NLB.