>How would one use this to call CQ ?
The simple answer is the same way you do/did with packet radio or any other digital mode.
Personally I haven't called CQ above 50 Mhz in years... but if you must...
Review how to embed messages in ping packets, and send a broadcast ping:
http://www.qsl.net/kb9mwr/projects/wireless/pingid.html
#!/bin/bash
MSG="CQ DE KB9MWR"
PATTERN=`echo -n "$MSG" |xxd -p`
/bin/ping -c 1 -p $PATTERN 44.92.255.255
eth1: len 60 4b:42:39:4d:57:52->6b:62:39:6d:77:72 type = IP
IP: len 42 44.92.20.35->44.92.255.255 ihl 20 ttl 64 prot ICMP
ICMP: type echo request id 54377 seq 0
Öùù CQ DE KB9MWR
Or perhaps you are seeking a voice QSO? Again, it seems much easier to plug in a pair of cheap Grandstream IP phones and dial the other end by IP address.
But if you must... review the CM-108 USB sound FOB.
The CM-108 FOB as detailed in the PDF is perfect for interfacing to FM rigs for repeater/simplex links.

Here I just wired an old microphone to a USB sound card.
The Ubiquiti Routerstation Pro has a USB port.

To get that USB sound to work review this:
http://sokrates.mimuw.edu.pl/~sebek/openwrt/
Then install and use something simple like Speakfreely.
Or how about an IRC or Jabber server?
The correct answer is how do you want to call CQ?
Perhaps you are contemplating a pair of 70cm Doodle Labs DL-435 cards? May I suggest you do your CQ as amateur digital video with Laptops running NetMeeting. (or the Linux equivalent for those in-the-know)
Antiquated Bandwidth rules do not apply when there is a video component.