Hi there, been playing Winston since Season 1 and have been in top 1000 Winston's since the game came out!
When playing against reaper you need an entirely different game sense. Similar to how you have to fight Genji, your entire playstyle now revolves around that Reaper. You will only be engaging a Reaper with another dps following you and need to master bubble strafing.
With a Reaper in play, two play styles develop. If the Reaper is overperforming and destroying the front lines, you need your teammates to focus fire him to force wraith. Once wraith has been popped, you can try leap melee to kill if he's low enough (Typically speaking, he will only wraith when hes low, meaning around 100ish health. If he does it any lower, just follow for kill similar to how Zarya charged is. Force her low health and when she pops bubble just focus her down) You must be perfect with your leap melee as your bubble must go down so that if he tries to shoot you he will shoot the bubble first.
If the Reaper is playing around you, meaning he's solely targetting you, you need to abuse his slow mobility and dive their backlines/straight up in the air depending on the fights. Diving the air is great as he has good damage drop off, it gives your mercy an escape, it puts the Reaper in an uncomfortable position of waiting for you to drop down and should be getting focused by your dps. Bubble strafing is hard to do but helps you live a hell of a lot longer in fights. You want this Reaper to solely target you. It's better for your team as he has long cooldowns and crappy mobility. Once wraith is popped, always try to follow and force the kill if it's safe.
I kinda feel this wasn't as accurate but I'll try to explain better through the eyes of genji vs winston. In that matchup, if the winston dives the genjis team, the genji must then dive that winstons team as hes hard to kill and should be winning most of his 1 vs 1s. If the genji is spacing properly and saving his dash for when the winston dives him, the fight is reset. If the genji keeps playing frontlines against you, you should have no problem forcing his dash , then leaping to punish. If the genji is flanking properly while you are diving, you need to start staying back more and saving your leap for when he tries to dash and escape.