Don't know about drum skills + a 388...
...but for tape mailing, here in the USA they have a special category called Medial Mail, it's a lower cost, and if I recall, you have to show them the contents before sealing it etc, because it may be a flat rate only for media...so they don't want people using it for other things.
Not sure what you have in the UK...and also, where are you shipping it to?
If it's outside the UK...you might just opt for FedEx.