If you need the cash, it's generally good to find a way to get the cash, unless the investor is extreme. It's always worse to raise cash when you are running out -- it's best to shore up cash when you have a buffer. Most professionals will say to always have a minimum of 9 months of cash. I frankly feel uncomfortable having less than 3 years of cash. You have to decide the buffer you want, but I think 15 months is my preferred minimum.
If you are worried about an investor being overbearing, here are a few ways to navigate. First, if you structure their investment in a founder-friendly way, you can protect against a lot of headaches. Specifically, if they invest in a market standard SAFE, that is a very founder friendly and protective. If they are investing as an equity investor, if they are not on your board and don't have special rights (protective provisions, information rights, board observer rights) -- and instead just passively investing -- they cannot have a legitimate claim to do much.
Having said that, any investor can file a lawsuit / be annoying if they wanted to after the fact -- even if they don't have any legal claim. If this is a concern, I would ask the investor for references. And specifically ask for references for founders where the investments did not create winners, and speak to those founders. Find out what the investor is like in times of stress. If they don't give you names of failed investments, make sure to find out from the given references who else you can call to diligence the investor.
If you are really worried and have enough cash, you can negotiate from a position of strength and just walk away if you can't strike a deal. For example, you can add a clause in the SAFE or Convertible Note that you can buy out the investor at your dsicretion by paying back the note / SAFE. Most notes / SAFEs will not have that language as a default -- and it's definitely non-standard language -- but if you are going to walk away anyways you can put that forward and see if they bite.
If the investor came through Alchemist, we also have leverage with their Vault profiel to try to protect our founders by disinviting or giving a negative review to any investor that's acvting badly.