There are a couple of supermarket sized Co-Op stores on Skye. One in Broadford next to the filling station & the other on the A87 Uig road just outside Portree.
Although there is no Tesco on the island, they do provide a click & collect service every day to the following drop-off points
Portree - Camanachd, Struan Road IV51 9EG
Broadford - Old Corrie Industrial Estate (next to Jewsons) IV49 9AB
The service is extremley popular, however, so you may need to book a slot a couple of weeks in advance.