I know you can OC your CPU to 4.5Ghz but if you're streaming a 4 threaded CPU is pretty bad.
I had no idea you streamed...that makes a huge difference. If that's important to you I'd want something like a 2700/x instead of a 4790k, the latter could do it but it totally depends on the performance you want while playing games and the desired stream quality. Basically you're asking your CPU to run a game while encoding a video which is possible with a lesser CPU but one or the other must suffer.
I've seen some people still using it without issue:
...but that heavily depends on what level of performance you're expecting.
If you're already streaming with your CPU, upgrading to a 4790k will give you 30% more CPU performance with the same clock speed.
Your CPU (if running stock) operates at 3.7Ghz with all cores under load so overclocking that to 4.5Ghz is a 20% bump in performance. Going from your CPU (stock) to an OC'd 4790k (4.5Ghz) gets you about a 50% bump in performance. I recently bought a 4790k and it and my 4690k were able to hit 4.5Ghz with a garbage 212 Evo without delidding and 4.7Ghz delidded. 4.5Ghz is a mild OC that any CPU should reach easily, even if it couldn't 4.4Ghz isn't a huge step back.
The GPU isn't going to effect your streaming much aside from the fact that you'll have better performance to run the game which is then used for the stream.
What resolution and framerate do you need and what games do you stream? This is a pretty important metric.
Your PSU is pretty much garbage in 2019 TBH, I wouldn't say that it's dangerous to use but it was only received well in 2013 because it was so cheap and had a 3 year warranty. Not sure if it was 3 years because they didn't want to deal with years of RMAs from a PSU that only cost $60 or because they didn't believe it would last for years and years. It's always your call but I wouldn't use it. Every component in your rig depends on hte PSU and the PSU has the power to destroy each component if something were to go wrong. Since you're about to invest more money into your PC I really wouldn't recommend using it.
FYI My 4790k with 16gb 2400Mhz Cas11 scores about 950
points in CinebenchR15 @ 4.7Ghz, x44 cache
Compare that to the chart and you'll see just how powerful something like a Ryzen 2600 can be for streaming on a budget.
A 4790k can still do the job IMO but there will be compromises and it may be more cost effective in the long run to upgrade to something like the 2600 or better. Obviously that means new ram and board though.