Go to a shop and order a set of $15 shifters. Then leave this bike as it is. It looks to be in great shape and attempting to convert it would probably be very time consuming and expensive.
The trick with shorter stack bolts on the crank only works with more modern cranksets. Modern cranks have a chainring on either side of the spider. The larger one is on the outside and the smaller on the inside. Generally the inside position will get you close to a straight chainline so people simply remove the outside ring and use shorter bolts. Your crank has both rings on the inside. If you remove the larger ring, you will have to put spacers on the bolts so that the smaller ring will remain in the same place.
If you really want to do it, take the rear wheel to a shop and have them remove the 5spd freewheel and install a SS freewheel. Then put the wheel back in the frame and see if it lines up with one of the chainrings. If it does, you can try removing the unused ring and replacing it with spacers. If it doesn't, you'd be better off getting a new bike. (Return the freewheel to the shop and have them put the 5spd back on the wheel. It'll probably cost about $10 in labor each time). That way, instead of having one bike that required a new crank or a respaced wheel, you'll have two bikes that are being used for their intended purpose.
Originally Posted by Josh Frank
I just wanna ride
Not sure if most cottered cranks are this way, but from experience my friend got a 1980's galaxy that we converted to fixed and within the first 6 months the bottom bracket started to give and was completely gone within 8 months. And it's being ridden by a very casual rider with both brakes that get used fairly often.
So you could use them, but plan to need to upgrade soon.