the only crawlies to be worried about is the time share touts, ive just got back and only saw 2 roaches and they was outside on the pavement

Hi, I have been to Tenerife many times and can honestly say I have never seen a spider or a wasp. Once, in around 12 visits I have seen a cockroach and the bar/restaurant dealt with it immediately. So I have been told you do see them around restaurants/kitchens but as I have siad, I have only seen the 1. I have only ever been bitten by a mosquito once as well, and that was when I did walk under some overhanging trees quite early in the morning and the watering system must have just finished working because the trees were dripping, so, I really don't think you will have much of a problem with them either. Hope this makes you feel better.