I do something like this in my development environment by configuring Apache on port 80 as a proxy for my application server on port 8080, with the following Apache config:
NameVirtualHost *
<VirtualHost *>
<Proxy http://127.0.0.1:8080/*>
Allow from all
</Proxy>
<LocationMatch "/myapp">
ProxyPass http://127.0.0.1:8080/myapp
ProxyPassReverse http://127.0.0.1:8080/myapp
Header add myheader "myvalue"
RequestHeader set myheader "myvalue"
</LocationMatch>
</VirtualHost>
See LocationMatch and RequestHeader documentation.
This adds the header myheader: myvalue to requests going to the application server.