This is a relatively small set of trees - the easiest solution would be to use an electric chainsaw like the DeWalt DCCS670T1 16" 60v or DCCS620B (DeWalt XR 12" 20v). Start by trimming the branches starting from as high up as you can reach, smaller to larger, and when you get down to the trunk cut 2 foot slices off so they are easily manageable. You want to try and remove as much of the branch as you can to eliminate the possibility of them getting snagged on you on the way down or entailed in your chainsaw.
You can use a hand axe or hand saw, but this is much more dangerous than a power chainsaw (surprisingly, yes - the chainsaw is safer in the hands of an educated individual who is trained in it's proper usage and using it properly).
Once you have the trunk down to about 2 feet off the ground, you will need to deal with the stump. There are various techniques to remove a stump, depending on how quickly you want it gone and how much effort, time, and money you want to spend. This being at your home, I would drill into it with a concrete / hammer drill and pour Epson salt, Vinegar or Baking Soda into the holes. It will take 8 - 10 weeks for it to erode the stump enough for you to pull it out and dispose of it as you see fit.
As far as disturbing the hydrangea - it depends on how the root systems interact. If you can avoid damaging the roots of the hydrangea, and the soil remains relatively solid (or you replace and repack the soil) the hydrangea will come out of it just fine.
Just avoid cutting into their roots as roots are like skin on humans and cutting into the root can invite infection and bacteria just like an open wound would do on you or I.
