If I understand the documentation correctly, you can use the interlock to switch the laser off. I can not find if it's sufficient reconnect the interlock to switch it on again or that you first have to switch to standby and next to on again.
Is the product that you have exactly the one pictured in the user manual? Because the use manual mentions a DB9 connector that is nowhere to be found in any of the images in the user manual.
I think that for your RS232 approach, table 2-5 and table 4-7 (sheet 1) apply with regards to connections. The USB is for communication with a USB host (an Arduino isn't unless you go through the trouble of adding a host shield and possibly a lot of coding).
I would contact the supplier / manufacturer to find out if the unit is true RS232 as it's not explicitly mentioned and the manual seems to consider RS232 as a protocol instead of a communication layer. RS232 uses usually around +12V and -12V (I think there is some variation possible like +3V .. +18V and -3V .. -18V) and the Arduino will not like that. You can also try to measure yourself; best with an oscilloscope; alternatively with a multimeter, if there is a negative voltage on the TX line while nothing is transmitted from the control unit, you know it's RS232.
Once they have confirmed that it's indeed RS232 levels and if the interlock does not work, the best solution is to get yourself a MAX232 (or similar; there are breakout boards) to convert TTL levels to RS232 levels.