Are These Brother Names at War with Each Other?
The meanings are not a big deal. Most people don't think of Mark as meaning "warlike" for several reasons: It's too common and classic a name for anyone to recall its etymology. The meaning isn't immediately obvious, as it would be in a word name; it comes via the Roman war god, Mars. Above all, the notion that Mark truly means "warlike" isn't terribly accurate. Yes, Mark comes from the Roman name Marcus. No one really knows the origin of that name, but scholars assume it indicated a connection or dedication to Mars. "Mars-like" or "faithful to Mars" might be a more direct interpretation.
So, problem solved, right? Not quite. In my opinion, what could be a big deal is giving one child a rare, eye-catching, contemporary name, and the other a super-familiar name that was a staple of the 1950s and '60s. That's the connection (or lack of one) that people might notice.
You're considering a big shift in baby-naming style from one child to the next. Is there a way to call a truce? Of course. You could decide that Mark is your favorite name, and that's that; maybe you'd give Mark a more contemporary or unusual middle name as a subtle link with Pax.
Or, look for another name that bridges the gap between contemporary and classic, one that's still simple and works with your last name.
August has the noun-like quality of Pax and the short nickname Gus; it's a name with a popularity trend inverse with Mark's (it bottomed out in the 1960s and recently shot upward). It's also on this list of "quirky classic" names for boys, which might be just the style you're looking for.
Beau is another word-y, one-syllable choice, but it may not meet your wish for a name that's easy to spell (unless you go with Bo).
Kai is a Scandinavian shortie that's on the rise (so it's recognizable) and shares the hard K sound with Mark.
Luke, like Mark, is one of the four evangelists in the Christian Bible, but its popularity curve is closer to Pax's than Mark's. Etymologically, Luke and Lucas may be tied with the Latin word "lux," meaning light—a nice complement to Pax. Leo, too, is short, sweet, and classic, yet feels more contemporary than Mark. (And Leo Tolstoy is the author of War and Peace!)
Zane contains that high-value letter Z, a tie-in with Pax’s X. Zeke, on its own or short for Ezekiel, is another way to get to Z, along with Zeb and Zev. A Q name, like Quinn, works the same way. It's simple, yet special; and whatever name you choose will soon be as special to you as Pax is now.