I would say the easiest way to do what you ask would be to let the emonTH → emonBase → emonCMS function normally and as intended, then with that data being available via the feeds api, you can write a small script or use node-red to query the data from emoncms as simply as
https://emoncms.org/feed/fetch.json?ids=101,102,103,104,105&apikey=abc123
where “101”,“102”, “103”,“104” and “105” are the feed ids for the metrics you want to share with WU and “abc123” is your emoncms apikey (in this case it can be either the readonly or the readwrite apikey)
Then parse the result eg
[15.6,16.1,16.7,21.1,50.0]
into an out-going WU api call such as
https://weatherstation.wunderground.com/weatherstation/updateweatherstation.php?ID=MYPWSID&PASSWORD=pa55w0rd&dateutc=now&tempf=60&temp1f=61&temp2f=62&indoortempf=70&indoorhumidity=50&action=updateraw
where “MYPWSID” and “pa55w0rd” are the ID and password for the Personal Weather Station (PWS) you create at WU and tempf, temp1f, temp2f, indoortempf and indoorhumidity,are the values retrieved from emoncms above, the temperature need converting from Celsius to Fahrenheit as WU only accepts F where as emoncms values are usually C (this can be altered in the sketch/firmware or even via the input processing if you prefer to persist data in F), the humidity is a percentage in both cases.
Info on the PWS api can found at http://help.wunderground.com/knowledgebase/articles/865575-pws-upload-protocol which also lists all the possible fields you can include.
This script could be run every 5mins by creating a cronjob or you would need to look at using a start up service and putting the code in a loop, the latter is only really worth doing if you are intending to update a lot more frequently, in which case you would need to use the “rapidfire” WU PWS api instead (details at the bottom of the linked PWS api page). As temperature and humidity are quite slow moving a 5min update is more than ample as WU only updates the data every 5min unless the “rapidfire” api is used for “realtime” data, I think “rapidfire” is more aimed at capturing rain fall and wind speed direction and speed etc,