Does chain width matter when choosing a sprocket or chainwheel?

I am planning on building a fixed gear bicycle from scratch. As I understand it, 1/8" inch chain should be used on a bicycle without a deraileur and 3/32" chain should be used if the bicycle does have one. But as I use only vintage parts when working on a bicycle, I don't think I could find a single cotterless chainwheel. Most singlechainwheels back then were made for cottered bottom brackets. What I want to know is, if the rear cog is designed for 1/8" chain, and the chain is 1/8", does it matter if the chainwheel was made for 3/32" chain?

You'll have no problem using a 1/8" chain with a 3/32" chainring as long as you don't have to shift.

What's all this talk about cotter pins and such! I rode and raced in the early 60s with a fixed bike, it had a single Stronglight Aluminium alloy chain ring and cotterless cranks. My Son is using the said bike at the moment on his commute to work. I think you could find a suitable chain ring, cranks and a bottom bracket on eBay under vintage parts.

Would a track set up not be suitable in your situation?

Yeah, you muts but matching gear cogs and chains. You can buy them in sets. I believe chimano make the best ones.

1/8 chain will work fine with a 3/32 cw, but can you still get cotter pins? and watch out for contintental size cotter pins, smaller than UK.

sorry ive never been part of the chain gang i wouldnt know