Find "Rose's door"
I mean this seriously, but figuratively.
In the movie, the floating door was how Rose survived. It was a literary device to allow a believable, yet unexpected way for her to live to tell her story.
Create "Rose's door" for your story. It could be a paddle, maybe some kind of semi-waterproof wrapping, a makeshift wetsuit, or even a buoyant bathtub. You might even survive by floating in your time machine itself.
That would be the "least likely to contaminate the timeline" while allowing you to be witness to more.
Think "fly on the wall", or "Rose on the door". Be creative and inventive.
Note on comedy:
If you are going for some comedy, you could make it an actual door, perhaps even drop a line, "I remember someone survived by floating on a door." Especially in time travel, some tongue-in-cheek humor makes the medicine go down. Comedy often plays a role in time travel, consider Back to the Future or Avengers: End Game where Captain America fights himself.