Hot sauce; Remove seeds? I use a recipe that calls for removing the top third or more of Cayenne peppers in order to remove most of the seeds. Seems like a waste to me. Aside from having to strain out the seeds after cooking, what would it hurt to just cut the stem and cook the peppers with the seeds in there? Would it have an ill affect on the taste? I wouldn't think so since the seeds are also used for crushed red pepper.
I just made a batch of hot sauce that was very cayenne-heavy myself. Keep the seeds. 

You want to get every last bit of heat out of those babies, especially if you are diluting with a significant amount of vinegar. 

The only use case I can think of for chopping the tops off as described in your recipe is if you aren't already planning to strain out the pulp as well. 

Even if I was eager to keep pulp but avoid seeds in my final batch I would rather scrape seeds from the individual peppers than waste that much product.

I personally don't think you'll notice any off flavors from the seeds.