As long as you TT no more than 2 days forward and backward, and you always run around and talk to all the villagers outside of their homes to make sure they don't plan on moving, you should be fine.
The key to TTing is actually knowing what you're doing. TTing has almost no negative side effects whatsoever if you actually do it properly.
Sorry for your loss though.
So guys, I need help now I don't want to do this wrong. I have 10 villagers rn and I want to get rid of one I don't really like by time travelling but I don't want to mess up because I always do. Should I time travel every day one by one and talk to only the villagers I like? or should I skip 2 and then go back... please help x_x
EDIT: nevermind, Rocket is moving out on the 27th in game, I'm on the 24th. Would it be safe to skip days?