I actually had the same question a couple of years back. so I tried it!
If you can do 25 Pushups already, the Fighter won't work for you. at least that's how it was for me at 15-20 Repmax.
For one arm Pushups, I reached 10 Repmax on both arms using a Scheme very similar to Fighter Pull-Up.
the three methods which helped me the most for conventional push-ups:
1.
Ethan Reeve's density training. Pick a RepMax goal, multiply by two. This is the total volume per session. start using sets of 2, starting a new set every minute, until you hit the desired volume. you then progress by "compressing", same volume, same timing, but sets of 3. Then sets of 4, 5, and so on. note that it is not 1 minute of rest, but 1 set every minute, so rest periods decrease with higher reps per set. train 2 times per week per exercise, no more than 2 exercises at once.
2.
"Arnolds 100 Pull-Ups, as explained by Matt Kroc", slightly modified by me: Do 200 push ups as fast as possible. try staying within a minimum of 1 minute rest and 5 reps at a time. this method took me from 35-ish to 80-ish within a month or two. It feels like a more fun and "pumpy" version of the formerly mentioned method, It tends to be more taxing though. train 1-2 times per week, depending on what else you're training.
3.
Inspired by GTG/hit the deck, but a thing of my own: 4 sets spread as evenly as possible throughout your waking hours. each set, you do as many as you can in that moment minus 5-10 reps. In a different year, took me from 20-ish to 60-ish within 1-2 month. Train 3 times a week or every other day.
Do note that all of these programs generate fatigue and sometimes muscle Ache. Not the PTTP / Fighter Pullup kind of thing. I don't think you would mind, but you will gain a good amount of muscle mass, especially on the first 2 programs if you eat enough protein and calories in general