> find one small
"Small" fans are usually a mistake. Size, airflow, and NOISE are related. You want a certain airflow. (We don't know how much, but more than gnat-blow.) Unless you only play VERY LOUD, you do not want noise. This leads to an "over-size" fan worked below design voltage.
"Oversize" because fan specifiers look to the air-flow first. (They won't be living with their product.) So fan makers rev-up the fans for big airflow, damn the noise (within limits). So for many living-with, working-with, and recording-with purposes, we take a "12V" fan and run it on 9V or 6V.
I had a net-hub made a hell of a racket. Meant to go in a hot server closet. But I had it in my office. Two 12V fans parallel on 12V. I re-rigged them series, they got 6V each. Were much quieter and the cooling was ample for office-temp air.
For the last 6 years I have had a Pentium PC, stock Intel fan cooler. Pretty darn loud. I'm re-purposing it, and the noise finally got to me. I've discovered it never gets ANYwhere near design max temperature. I pulled the fan and it didn't hot-up frighteningly fast.
I just left it run for hours with 90 Ohms in series with the fan. That gives 6.1V, about half RPM, and MUCH less noise. It shows 14C rise, and 63C rise is allowable (22C room, 85C max inside CPU). I just bumped the resistor to 135 Ohms (I had a 4-pack of 270r) which makes it *silent* (to my ear) and will see how toasty it gets. I suspect <20C rise, assume 30C in summer, 50C is still far below the CPU's limit. I wish I had done this 6 years ago. (But I still had Intel's warranty then.)
This is a nice 3.5" fan and probably a 65 Watt CPU. This is not out of sight of the heat in a AC30 (perhaps 90 Watts), and tube-stuff can certainly live long and prosper at max CPU temperature. So I'd be thinking of 3" fan, perhaps 2" if in a real tight spot and I was not sleeping in the same room. And of course, run the fan on lower voltage. If you only have "rated voltages (as in my PC), a handful of 270 or 330 is a good trimmer resistor. As noted, 6.3VAC rectified on a cap is 7V or 8V, which is a good starting zone for less-loud.
This good CPU cooler fan drew 0.12 Amps at 11.9VDC. Seems to be 0.068A at ~~6.1VDC. For hasty guesswork, pretend it is 100 Ohms and use divider-law. Small 12V fans will be higher "resistance". 5V fans will be lower "resistance". Teeny 5V fans may get back near 100 Ohms, but for any useful airflow a teeny-tiny fan is more noise than you want.