I am trying to construct an itinerary with SAS and would like to know on which weekdays they operate transatlantic flights (in my case in April 2016). I was hoping to find something like (unverified example ahead):

CPH - BOS: M--TFSS

CPH - EWR: M--TFS-

indicating that there are connections from Copenhagen to Boston on all days of the week except Tuesdays and Wednesdays and to New York (Newark) on Mondays, Thursdays, Fridays and Saturdays.

The closest I could come to is this flight search tool on their website but that requires me to enter a date (week), an origin (which I'd like to leave open) plus the website then times out on me.

One way is to use Google Flights. It won't give you a plaintext schedule, but you can see which days flights operate on quite easily through a visualization they provide.

Finding the days a specific route flies

Search for your origin and destination, specify the airline you want to check, filter for your nonstop flights, and then expand the calendar by clicking out and endpoints, It will only show flights with available seats, so some days with an operating but full flight will show up as blank, but it's pretty rare for a flight a month or two in advance to be completely sold out.

Here's the search for CPH-EWR with the settings I detailed above:

And here's the result for CPH-BOS:

Expanding to all transatlantic routes from SAS hubs

To find out which direct transatlantic routes SAS flies, you can use Google Flight's "Discover trips" feature. Selecting the same filters as before (SAS, Nonstop) but expanding the origin to CPH, ARN, OSL (SAS's hubs) and the destination to "United States", you'll get a list of SAS's destinations in the US serviced by direct transatlantic flighs:

Then, you can examine the calendars for each of these destinations individually, or for any subset of up to five destinations.