Great to know that NGROK works with DNN. That being the case it only remains to determine why it does not work for me. 

Here is the process that I am using.

Step 1)

Start the NGROK process

>ngrok http -region eu -host-header=bwig.pq.v04.01.d804.local 80

ngrok by @inconshreveable                                                                                 (Ctrl+C to quit)

Session Status             online
Account                       Daniel Bigelow (Plan: Free)
Version                       2.1.18
Region                        Europe (eu)
Web Interface                http://127.0.0.1:4040
Forwarding                    http://d7e629fb.eu.ngrok.io -> localhost:80
Forwarding                    https://d7e629fb.eu.ngrok.io -> localhost:80

Connections                   ttl     opn     rt1     rt5     p50     p90

                              0       0       0.00    0.00    0.00    0.00   

Step 2) 
Add the URL d7e629fb.eu.ngrok.io as a primary site alias, and for good measure also

d7e629fb.eu.ngrok.io/en
d7e629fb.eu.ngrok.io/de
then click Update

Step 3)
Connect NGROK to the running DNN instance on localhost by entering http://d7e629fb.eu.ngrok.io/en/ in the address field of a browser.

Step 4)
Observe that the home page of the website running on localhost appears in the browser at the URL in step 3.
GREAT

Step 5)
Click the Modules link.
The new page appears via localhost at URL: http://bwig.pq.v04.01.d804.local/en/Modules
BAD

Step 6)
In the address field, type Modules after http://d7e629fb.eu.ngrok.io/en/ to specify the URL to get 
http://d7e629fb.eu.ngrok.io/en/Modules
The new page appears via NGROK at URL: http://d7e629fb.eu.ngrok.io/en/Modules
GOOD, however this required a manual entry. Not really what I wanted.

As mentioned previously, when I hover over a DDR menu item the domain part of the URL (as shown in the bottom left of the window) is the localhost domain. Hence, it is not surprising that the page opens directly on localhost when the DDR link is clicked.

Any suggestions?

Daniel