Peggy and Shasta bantered back and forth from the palace all the way to the markets. Most of the places that Skye wanted to take Shasta to were clustered in the same area. Once they had arrived at the first shop, the four could easily walk to the others, and have a bit of time to spare.
The shops were mostly owned by Fae, so Karena wouldn't be able to tamper with their orders in any way. Thanks to her Shaman rounds, there were few people that would turn away a favor to Skye. The only way most would was if it endangered their livelihoods.
Karena had influence and power due to her future as Queen of Alcon, but it was also common knowledge that Skye was favored by Magnus. If complaints were brought against her, and Skye vouched for the validity of those claims: Magnus would side with Skye and the shop owners.