What I did when I was looking overseas was to only send out letters and CVs for posted jobs. If the posting was handled by an agent, then it's ok to send a general letter or query to the agent or agency, since they can certainly advise you if they have other postings that might be of interest.

I used to get lots of unsolicited job queries when I was working in Germany and yes, those can get to be off-putting. But if you work through the various online sites and target specific postings or agencies that handle the types of jobs that interest you, it should be ok.
Cheers,
Bev