Amazon web services – AWS – EC2: how to use a different public address for outgoing connections

I have an instance of AWS Ubuntu EC2 with an assigned elastic IP address and running a web application.

I would like to run a web crawl script on my server and I do not prefer that my server / domain be crawled from the IP address that my script connects to external websites.

For this purpose, I decided to enable and use a NAT gateway in the VPC. However, when I changed the default route in the VPC to the NAT gateway, I also lost the connection to my own server.

Will I appreciate here if you can guide me to create a solution through the NAT gateway or in some other way?