No, mystery islands are random whether you have the tools for them or not.
Any small/one higher level islands still aren't horrible to modify for bug catching, just completely clear off the cliffs and run by every once in awhile to scare off any crawling bug spawns there~
Not necessarily. There are a few islands with cliffs that may show up if you don't have a ladder. Also a ladder is needed for the 2% chance to get Tree Island which is the best place to hunt for tree beetles, if those are what you need.
Some islands are only available if you have a ladder, but even if you don't have a ladder, you'll still find some that are not flat. This shows the probability of getting each island with and without a ladder:
My friend got stuck on a hunt last week with a tiered island and no ladder. Thankfully is was not someone they wanted! I always make sure to take a ladder on hunts just in case. You can always make one once you're there, though! That is, if you bring an axe or the types of wood you need!