Any screw can be modified to make it self-tapping and the process is surprisingly easy. All that's required is to create one or more cutting edges and the clearance needed for the swarf, and the existing threading takes care of the rest (just as it does with manufactured self-tapping screws).
The modification necessary can be a very quick operation, literally a few seconds per screw at fastest. Even the slowest method really only requires a modest effort, taking at most a couple of minutes.
This simplest method it to sand or grind the side of the screw; grip your screw in gloved fingers or pliers (pad jaws to prevent crushing the threads) and hold it against a belt sander or grinder until a flat face has been created that is approximately 1/3 of the way up the threads. Ideally it should retain its original point, looking something like this when you're done:
Another method more directly copies the form of commercial self-tapping screws, where you create a groove down the side of the screw somewhat like this:
As most screws are made of mild steel this can be done using any common triangular needle or warding file, or a Western saw-sharpening file. For those with a Dremel-type mini drill a cutting disk/slitting disk can be used to do a similar job but care must be taken not to cut too deeply.
Once modified in either of these ways a screw can usually (not always) be driven in and left there as the fastener, without any compromise in holding power. But alternatively the one screw can be used repeatedly, i.e. used as a threading tool. After driving home it can be backed out of the hole and an unmodified screw of the same type driven in its place; so within reason this modification might only need to be done once per screw type for any project.
Note: it is probably best not to try to convert brass screws, it is likely they will not be strong enough to take the strain and they could easily snap in half when being driven into the wood.
As I was pulling together images for this Answer I discovered that, no surprise, this tip is nothing new. Here's a mention of it in Popular Mechanics from November 1923:
Bonus related point — threading holes
A similar process can actually be used on anything with a thread to allow you to tap a thread in a drilled hole of suitable diameter. This can be done with bolts of course, but just a length of threaded rod (including acme-threaded rod as commonly used in bench vices) can be modified in the same way, to tap wood and other softer materials such as the harder plastics used for some jigs and accessories, as well as aluminium.
Although some modern guides suggest grinding substantial grooves down the length of your bolt/threaded rod, it is far simpler and easier to file, sand or grind 2-4 flats onto the lower portion of the bolt or threaded rod, as in either of these examples: