Is there a more elegant way to remotely run chef-client?

That'd pretty much how you get things started to begin with, but it only needs to be done once. The initial run of chef-client typically enables and starts the chef-client daemon as an init.d service.

If you really wanted to do it more elegantly, you could ditch knife-ssh and run ssh directly:

ssh ubuntu@ipadddress -i mycredentials.pem sudo chef-client

that will probably be faster, as knife-ssh does a search against the Chef server to fetch nodes matching the search term (in this case name:dynode), which you don't strictly need to do if you already know the IP address.

You could use knife ssh to run chef-client on all boxes that contain a certain role or recipe:

knife ssh "role:web" "sudo chef-client" -x ubuntu --sudo 

Or if you're in EC2:

knife ssh "role:web" "sudo chef-client" -x ubuntu -a ec2.public_hostname