The 100 ohm resistor will probably be in line ie in series and is just a current limiter to protect the pwm output pin. With the laser flashing during the nano boot there probably isn’t a pull down resistor that I was postulating may be causing your problem…so…I can’t think of anything else offhand…how many spare nanos do you have? Remove the Nano and use a jumper lead to flash +5v onto the D11 pin socket…the laser should fire…if it does the problem is the pwm signal from the Nano and the board is ok.
For a cheap scope I use one of these. you can either buy it as a kit (just make sure the surface mount components have been mounted) or you can get them ready made, some even come in a case!!! I fitted a minute 2S lipo in mine with the balance lead hanging out the bottom.
There are also software based scopes that will do a good enough job for this type of application, This Espotek offering is a good example…one of our co-forumists has received one and done some experimenting with it here
I have no experience with endoscopes other than there used to be a problem with MediaTek chipset mobile phones not working with usb endoscopes, but that was some time ago and may well have been sorted out.