Assuming you have a SOHO router what you are proposing won't work, but there is a solution.
The issue you will come across is that you are trying to bind multiple IP addresses to a single machine, and have different websites on each. There is no problem doing this - however your SOHO router will probably only be able to map 1 IP address on port 80.
The solution is to have multiple websites on the same internal IP address - and this is a common configuration, and has been supported since RFC2068 in 1997. The way this works is that all the websites point to the same IP address, and the first thing they do when they connect is advise what domain name they wanted. This is called Name Based Virtual hosting.
To do this in Apache you need the following directives:
Ensure the directive "NameVirtualHost X.X.X.X" is in your apache configuration file - this is the internal IP address that the webserver is running on.
Then, for each website, set up a virtualhost folder like
ServerAlias domain.name.of.website alt.domain.name.of.website
(Other directives specific to site here)
Note that the ServerAlias directive is optional.
Also note that you can do a similar thing with HTTPS hosting on port 443, but needs to specify certificate keys etc as well, and this will only work for newer (Windows 7 and above) systems.