I’m assuming your shop has official independent Charity status that is recognised by HMRC and the Charities Commission and not just a shop that passes on its takings to the former major Charity.
Setting up Gift Aid is a legal process and quite a responsibility for a volunteer. There is guidance from HMRC so it is possible. It is the ongoing commitment of registering each donor and donation, ongoing as each new donor joins, producing the spreadsheets for HMRC and making the claims, informing each donor of their contribution, that is time consuming.
I think you would need a volunteer who is willing to commit a number of hours on a weekly basis and to take on not just the process but also the legal responsibilities. It would be very easy to get in a muddle if it was done on an occasional basis or if it was shared amongst all volunteers.
Unless you have someone who has had similar responsibilities in a past job, I can see that most volunteers would be reluctant.
I have done similar work in the past but I wouldn’t want the responsibility and ongoing time commitment now.