First of all, does the civilian airfield have air traffic control? If they do, you might find that the controllers have a directly link to the MATZ controllers, and can negotiate on your behalf while you're on their frequency. In any case, if they have ATC, give them a call and ask the controllers for advice. I've always found controllers more than willing to answer questions on the phone.
If it's not ATC, it's a bit more tricky since you'll have to negotiate it yourself. Still worth ringing the airport and finding out what local pilots do, or ringing the MATZ controller for advice, though.
In general, I wouldn't go for either of your options. I'd call up the civil airfield well before reaching them, ask permission to transit their ATZ, then request or report (depending whether ATC or not) a frequency change to the MATZ frequency well before reaching the MATZ. That might mean you leave the ATZ's frequency before leaving it, maybe even before entering it, but as long as you've got enough information to be able to pass over the airfield safely, that's fine.
Another option, of course, would be to go around the side of the ATZ!
FFF
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