Hi there,

Yes this would be doable with a reverse proxy setup with Nginx. The Nginx server block configuration will look something like this:

server {
    listen 80;
    server_name your_domain.com www.your_domain.com;

    location /arbitrary_id_1 {
        proxy_pass http://droplet_ip;
        proxy_set_header Host $host;
        proxy_set_header X-Real-IP $remote_addr;
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header X-Forwarded-Proto $scheme;
    }

    location /arbitrary_id_2 {
        proxy_pass http://droplet_ip;
        proxy_set_header Host $host;
        proxy_set_header X-Real-IP $remote_addr;
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header X-Forwarded-Proto $scheme;
    }
}

For more information I could suggest this tutorial here:

https://www.digitalocean.com/community/tutorials/how-to-configure-nginx-as-a-web-server-and-reverse-proxy-for-apache-on-one-ubuntu-18-04-server

Hope that this helps!
Regards,
Bobby