VPN with static public IP to connect to customer's apps

Yes that will work and is possible.

Do your users work from an office currently or are they all remote?

This post might help if you are planning on using Client VPN + NAT Gateway for a Static IP for VPN users.

How can a Client VPN user get a static IP address to access the internet? https://repost.aws/knowledge-center/client-vpn-static-ip-address