I'll go so far to say, there will be no other way to not have your board crack unless you use the threaded standoffs to mount the sockets. I've used perf board for years and years (though not at all lately) and I will tell you, plenty of times drilling even a 3/16" hole through the stuff, the drill just grabs the material and cracks it. Very irritating. Other than that it's ideal, LOL.
The Dremel with an abrasive (not a cutter) bit is likely the only way you'll achieve big (tube socket) holes successfully. And you may want to leave the overall size of the perf uncut until your wiring is done so that you are not fooling around with the mat'l with 3/4" of margin between the cutout hole and the edge of the perf. When you are finally done, THEN you cut down the size of the perf to match however much room you used for the project. The way you cut it is to score it w/xacto knife along a row of holes and snap it along the score-mark. Works perfect. Make sure you are on a non-giving solid surface (eg; not corrugated cardboard, shirt-cardboard is good) when you score it. I suppose you could score it with a side cutting Dremel bit, as well. Not a hacksaw! If you simply must use a hacksaw, you clamp the hacksaw in a vise upside down (eg; blade up) and move the mat'l against the blade and carefully hold the material on both sides of cut as you make the cut. Cut at a very acute angle. Likewise, if you don't like the choppy edge you get from scoring-and-breaking, don't try to file the material in the conventional way---get a largish flat file and move the material against the file. You just have to realize, any metal thing you bring up against the perf board outweighs it 500:1 and will just grab it and rip the heck out of it. It's amazing, really, to think of all the things I built using perf over the years...but it is phenomenally unfriendly to careless drilling. Each and every time I had a screwup, it was because of trying to drill the stuff without taking surgical precautions. Even careful drilling, you make 3-4 holes, get a little overconfident, then wham!
There is one other approach which I will bring up; though it is sort of ugly, it offers IMO the smallest chance of cracking the perf. That is to use conventional sockets, do not make big holes in the board, mount those sockets on let's say 3/4" standoffs above the board, and use tiny pieces of stiff bare wire to thread and loop through the tube terminals. By the time you have 9 loops going thru the tube terminals, the tube socket will be fairly rigidly mounted to the perf. Stuff & wire up your board. Now, using a short piece of 4-40 threaded rod which you'll likely have to cut from a long screw, use threaded standoffs UNDER the board to mount the thing to your enclosure. You will have to fabricate those pieces of threaded rod but that's no more work than surgically making huge holes in the perf.
All you ever wanted to know about perf. The stuff HATES being drilled.