Stick on WW's are much softer and closer to pure. If you melted it all together you would get a medium-soft alloy that would likely still work. Lead shot is usually quite hard to prevent it from deforming so I don't think your softer alloy, if mixed, would be ideal but would definitely still work. I wouldn't use it for competition or anything though.
Make sure you check your prices though. A shot maker can be quite an investment to buy or build and the cost of bulk target load by the flat is quite cheap. I know if you're buying premade lead shot it costs more to reload than to buy factory target load but I don't know what your pricing would be like.
300lbs of lead can load around 4200 shells with 1-1/8oz loads, depending on how much is lost in the process (oxidization, contamination, spillage, etc.).
4200 primers at $.05/each would be ~$210
15gr loads of $40/lbs powder for 4200 shells would be ~$360
Wads at $15/250 would be ~$260
I'll assume hulls are free (collected from a local range).
I also assume you already have a press.
I also don't account for your time.
So ~$830 for components to reload those.
At $72/flat you'd be looking at somewhere around $1200 to buy that many target load shells.
That leaves ~$370 to buy a shotmaker, heater, and energy for heating source (propane, electricity, etc.) and still break even. Last shot maker I was looking at was over $500 so it wouldn't be possible but I'm not familiar with the full range of prices out there.
Of course you can tailor loads specific to your needs and the loads you want may be prohibitively expensive. I know international loads (for ISSF/Olympic regulation trap and skeet) can be $200/flat or nearly $1/shell.
I'm not saying you shouldn't do it but just to do your math and look at your options ahead of time rather than regretting it half way through.
