Don't murder them, you've posted it on here - you'll be the prime suspect now.
Plan A
Every time you talk to her, hum under your breath. Do this every time you are within hearing distance. Encourage others to do likewise.
Deny you are doing anything, if questioned.
Eventually she will become accustomed to the sound of light hum and stop being such a princess about it.
Plan B
Do as much loud DIY as you possibly can, preferably in the garden. Do it within the noise pollution allowances so it is legal. Make as much noise as possible. I suggest pneumatic drilling, lawn mowing, strimmer, trimmer, hammering.
Do this with windows open, or even better, in the garden.
Continue for 6 months. Every day.
For a less realistic, but easier approach, tape a day of it and then play it on repeat. A kind of construction version of whale music.
After 6 months stop.
She will be gagging for the bliss of a Dysons soft hum.
Plan C
Tell her to stop being such a wankbadger and point out that unless she wishes to live on her own in a hut, she will have to cope with the noise of other things.
Then find as many brochures on manor estates, huts, private islands and shacks in the woods and post them through her door.