Need help with bonus items for a promotion

Running a black friday sale coming up. We have some cheap physical items that we can add as a bonus but we only have 10. We'd have to buy/ship them after 10 sales. The cost of the physical items is around $8 and shipping will vary but probably around $5 average.

I also have a digital download as bonus item #2 which is alot cheaper.

Our core offer is a year membership to our music lesson site for $47 (normally $124).

My question is this: How important is a physical item being included in a sale? An option we are looking at is to just give a $10 certificate from a music retailer instead of shipping them a physical bonus item. But something doesn't seem right to me with that. Why not just discount the price to $37 at that point? The physical item seems more tempting to me.

Another option is to just offer the physical bonus to the first 10 and then remove it from the page.

Would love some feedback on this as I don't know which way to go. We are trying to make some money from this but also "over deliver" to ensure that we have a good sale and people actually bite.

Thanks,

Aaron