Ok, so, to answer your specific question, the you need to set the umask to 000. If you want, I can give you those instructions. But I don't think that's what you want. Seriously.
Incidentally, the proxy_store_access configuration affects files created by both the proxy_store and proxy_cache systems (I checked this in the source code).
I don't mean to be rude, but I don't think you want to do what you're suggesting. I suspect you want to clean out your nginx chache regularily. If you look at the documentation here: http://nginx.org/en/docs/http/ngx_http_proxy_module.html#proxy_cache_path you'll see that there nginx should handle invalidating your cache to keep it under a certain size.
Now, if you still want to write a process that invalidates (I assume you mean deletes) the cache, here's a different option. If this is to run as a cronjob, put it in the nginx user's crontab. Also, there are ways to use sudo to give someone limited access to elevated permissions. Lastly, if you're really coding up a special program, then look into the setuid (aka suid) bit on the executable.
Good Luck. Does this help?