I hate to rain on your parade, but no lasing in a low flow cell with a CW pump.
For cw lasing of a dye you need flow to avoid triplet state quenching. You need to get the dye out of the lasing area very fast, or the molecules that just lased become adsorbers and block lasing. The time period you have is about a microsecond to clean out the lasing volume.
Typical dye jets are a 1 mm wide flat stream pumped at 60-80 PSI. The one CW dye laser I have thresholds at 3.6 watts.
If you had a qswitched pump with high peak power, you can switch to a low flow cell. Ie a 7 nanosecond pulse from a fast, doubled, Nd;YAG expends all its energy lasing before the triplet states form in the molecule. This is why a nitrogen laser with its high peak power can lase a dye. A small nitrogen laser might have a tenth of a milliwatt average power, but can have a 20-100 kilowatt peak power.
So your option as a hobbyist is to build a nitrogen laser to pump your dye cell, the cw 532 will just make it glow. Even if you gated your 500 mW on and off in a microsecond, you still would not have enough peak power to lase.
Your other option would be something like this:
Large High Power Xenon Strobe Tube-The Electronic Goldmine
A large xenon flashlamp firing a few shots a minute.
If you wish to do a flashlamp pumped laser, the Lankard design in Scientific American magazine works, but it would work better if you placed a IR adsorber around the lamp to damp the thermal shockwave from lamp, which tends to quench lasing.
Sorry,
Steve