1960s Falcon Track Bike - The British Italian Job

Regarding components I know the following:

• Hubs are Record Pista 36h with an 17t cog.
  
• The seatpost is a Nuovo Record.
  
• Stem Looks like a Cinelli 1a, might be a 2a if I'm lucky.
  
• Bars look like Cinelli Criterium pista (?)
  
• Unfortunately the NDS crank arm & pedal on it are missing, so I'm forced to get a pair of cranks and pedals.
  
  

Plan for the build is to get it up and running while not spending too much Money. That means that I will have to settle for some non-pista cranks. I could either spend around 60€ for a pair of super record strada cranks or I could get a pair of SR Apex cranks for 20€. I found some mks sylvan track pedals with Cages for 35€ and I think I'll probably get them.

The cranks lead me to the following question: in how far is it possible to use a strada crank on a track bike. How much of a difference is there as regards dishing, will it fuck up the chainline? Do I Need a new BB? Is it a stupid idea in the first place? Any advice would be appreciated!