Don’t ! Make a simple punch. Noel.

A finger plate is ideal for this, you can make a fancy one or do as I do and simply have a bit of flat stock with some tapped holes in it and use a screw and small clamp bar. A Vee ended clamp bar will be best for this as you can hold the strip either side of the hole. Even a piece of MDF, a wood screw and quickly knocked up clamp plate wil do.

Punching can often deform the soft brass not only the back of the hole but the width can bulge particularly if it is only 3mm wide like I tend to use mostly.

Also backing off the drill edges to give them a shallower, or nil, rake will reduce the chance of the brass grabbing and trying to climb the flutes.

Depending on the size you need, a small-diameter step-drill may be better than a twist-drill, though might not be available down to the diameter you need. (These are made for drilling sheet material.)

Drill into a suitable backing plate: e.g. some scrap plywood, MDF, off-cut of laminated chipboard.

Punches work well on thin metal but who has them in their home workshop?

Sandwich between 2 sacrificial pieces (as comment above) is a simple method.  The sacrificial pieces could also be used as a jig for drilling additional holes in the same position on other banding.

The forked end of the clamp is not far off sandwiching, you are clamping the work down flat to something and the fork is like a top plate and just leaves enough room for you to see your punch mark and fit the drill bit in position.

Yes  well made punch and close fitting die/plates won’t burr the work but comes down to whether you are the type that wants to get a project done or start another to complete the first. You would also need a way to position the strip in the die as you can’t see what you are doing.

Michael, what size strip and hole are you talking of? I typically use 3mm wide strip and 1.6mm holes, quite often drilling after bending.