I am sorry, but in order to prevent botulism, since cucumbers are a low acid vegetable, you need at least half of the brine as 5% acidity vinegar to water ratio. The old recipes were based on vinegers that were anywhere from 7% to 40% acidity. Other than that, I am sure they are very good.
Alum is not needed and will not keep quick pack pickles crisp. It can actually make them softer as they sit in the jars. It only works for fermented pickles. The new product, Pickle Crisp works well and is used by the commercial industry, too. It is calcium chloride.
You can buy it in the stores with canning supplies.

The other option to help crispness is to soak the cukes in a pickling lime solution. This is also an old practice, but sometimes still used today. Mrs. Wages still makes pickling lime. The cukes have to get both ends trimmed off and soaked in a non reactive pot or container. The lime solution must be thoroughly rinsed off afterwards, and before they are packed in jars and filled with the brine. The recipe above, would be much safer with at least 2 quarts vinegar and less than 2 quarts water. Plain salt, is not recommended either as it can still can contain anti-caking additives. Pure pickling salt is preferred over most any other salt. Kosher is an option to, provided it also has no other additives including iodine.

As to Ball Pickle Crisp, I have used this, as well as the bulk product from Bulk Foods. The latter is a courser product, so slightly more is needed per pint or quart jar.

Just for the record, though, fermented pickles definitely do not need alum and I never use it. I'm a new gardener, but an expert "fermenter" :) and to get crispy pickles, all you need to add is a little piece of horseradish or a few grape or oak leaves.

And if you're able to store fermented veggies in a fridge or other very cool environment, they're also healthier than veggies preserved with vinegar, since storing them that way means you don't have to kill all the beneficial fermenting microorganisms in a water bath. Those little beasties reduce the risk of diarrhea, food allergies, eczema and other ailments. Why pay for probiotics when you can make them yourself and they taste so good? Yummmmm!