OP, I know exactly where you are coming from. I actually wasn't too fond of Grimmy either back in the TS1 days. Skeletons in general always freaked me out a bit, especially as a child. I even chose not to install Livin' Large when re-installing my game because I just didn't want to have him there. (I also remember trying to install a mod that replaced him with an "angel of death", but being 12 years old and having no understanding of how Sims mods worked it didn't go so well.)
When TS2 came along and Grimmy became base game content, I had a modded painting that I used to stop Sims from aging to elder so I could experience the rest of the aging cycle without him appearing. But then I decided I wanted to start a Prosperity challenge. Prosperity is a generational challenge, kind of a rotational version of a Legacy, so if I wanted to do it properly I had to let Sims die of old age. I also decided to blog my challenge, which meant that I had to document the deaths somehow; I couldn't just scroll to another part of the screen until it was over. I ended up having to gradually desensitize myself. The first time an elder died of old age, I zoomed out as far as the camera would allow so he only appeared as a gray dot. Each time afterward, I tried to move the camera a little bit closer, until I didn't need to move the camera away at all. (The fact that you could no longer see the skull inside the hood helped a great deal too. The less skeletal, the better.)
Granted, in TS2 Grimmy's animations were more silly at times, especially for old age deaths and pet deaths. The TS4 "reaping" animation still startles me a bit, and I still tend to hit fast forward through it once I've gotten the necessary screenshots to document the death. I would advise against intentionally toggling many deaths in a row to "force" yourself to get over the fear. Don't make you're entire gameplay experience about Sim deaths. Play the game normally, maybe creating some households with elders as TS4 provides plenty of warning when a Sim is going to die from old age. When it happens, zoom out. Scroll farther away and watch from the public space. (TS2 didn't provide this option.) Hit fast forward if you need to. Once it's over, go back to playing your game. Eventually it will get easier. You may never love the character, but you'll be able to play the game without panicking. Alternatively, you could also watch YouTube clips of Sims dying in other people's games to desensitize yourself. Maybe let the audio play from another tab at first, then watch the video.
It also may help to learn about the concept/character of the Grim Reaper outside of The Sims; it may be less frightening if you can see the cultural history behind the character. (This helped me out a great deal as well.)
Of course, you may still play doing everything possible to keep your Sims alive and that's ok. And you may choose to play with aging off so your Sims don't die from old age, which is fine too. If it wasn't, that option wouldn't be in the game. While I still do let my Sims die of old age, I also don't intentionally lock them in a pool or set them on fire. And if they go into the "Mortified" or "Hysterical" emotions, you can bet I do everything in my power to bring that down. But I don't have anxiety any time I'm on a lot with an elder on it anymore.
