This depends on your router. If it can operate as a "gateway" and pass traffic through then this is possible and you can give your fedora box a routable ip address.
This is how a lot of people running netopia routers on T1 lines do exactly what you are talking about.
I don't recall ever seeing a netgear router that had a gateway mode, and doing it requires at lease a small segment, not just one address. I think it would take 4 addresses minium, and your ISP would have to know that you were running in a gateway mode. But yes, there is a way.
It sounds like your problem is you want to be able to say http::www.myhost.com
from inside and outside your network and go to the same apache server. This can be done another way. First, the public address outside is pretty normal, and you've got it working. Inside your network you just need to make a translation to show that on your LAN www.myhost.com
has a different IP than it does from the Internet. The easiest way is to make an entry in the /etc/hosts file that tells your local machine something like this:
*you may need to make that www.myhost.com
Now when you try to go to myhost.com your browser will not go to DNS to get the address, it will get it locally from the hosts file. This is ok for a desktop machine on your LAN but laptops are a different story because they might be inside or outside the LAN.
This means you need a more complicated fix. A simple one would be to write a script to change the hosts file. A robust solution would be to install your own DNS server on your LAN and then let it intercept DNS calls trying to lookup myhost.com and send you the local address.
With a DNS server the laptop and all machines on the LAN will automatically get the correct address from the LAN side when they are on the LAN with no modifications to their configuration or hosts file.
The problem is that setting up a DNS server will take a bit of study. I suggest using a program called Webmin if you decide to go this route.
There are two other things that might work without resorting to running DNS locally.
One is using static routes in the netgear box, and the other is using a routiing protocol (RIP). Years ago I spent some time doing it this way but ultimately I went to a private DNS. Either way its a lot of work for a simple problem.
The most elegant solution is to make your Apache box a router as well as a webserver and build the firewall/configuration with FWBuilder.
With FWBuilder you can intercept traffic heading for your static ip address and send it to apache on the local machine by changing its destination using iptables. This is incredibly flexible and learning how to do this is probably going to help you in other areas in the future. That would be my recommendation because its cheap, it will work, once you learn to use FWBuilder its easy to do, easy to document, and easy to figure out what you did 2 years later, and you can do hundreds of other things with it.