I'm sure this is basic, and looking at prior posts (and speaking with my son who was lucky enough to live in London for three years) I believe the general rule for US buyers of CWs is to use a credit card that does not charge an FX conversion fee and buy in GBP--seems everyone is convinced that will result in a lower cost purchase. That's easy.
My (new) question is from today's purchase of a Vintage Oak Leather Strap. Looking at the CW site in USD it showed $37.50 earlier, and £30. So I ordered it as GBP and by the time I hit checkout it was priced at £25! Then, in the email confirmation it shows £26.66! And, now that I re-checked USD the price is up to £39 and $48. Talk about hitting a moving target!
I know that FX rates change second-by-second, but I'm thinking that's not what's happening on the CW site? Or is it?
If someone can help me better understand what I saw today that would be helpful (not that I anticipate making any future expensive CW purchases after picking up my first two last week, mind you... this is purely an academic exercise, and no one (including my better half) should be thinking I'm hooked on CW

Many thanks!