I mix and match between metric and imperial drills to get the best fit that I can. I find that in wood, holes tend to tighten up slightly, every bit as much of a PITA as when drilling metal. A 10mm tube won't go through a 10mm hole unless your drill is really sloppy and is cutting oversize. I always aim to use about a 0.1mm bigger drill than the pin/tube stock. That gives a reasonable slide fit, not so tight it has to be hammered, just pushed firmly.
1/4 = 6.35mm, hence use a 6.4 or 6.5 drill. I tend to use the 6.4 and put up with it being a little tight, rather than 6.5 and having it be loose.
The conversion is 1 inch = 25.4mm, so, 7/16 = 11.1125mm which isn't aproximately 10 anything.
No amount of trying will make 7/16 stock go through a 10mm hole! and the other way around will be sloppy. If my tube was 7/16 I would buy a 11.2mm drill, which can be done from good engineering shops, or Axminster, or Cromwell.
Mind you, I would think that tube that size would be a bit big. I really like the way that tube of about 8mm diameter looks, I have also seen 1/4 inch tube look alright. The main problem I find is getting the tube to have adequate wall thickness to chamfer. The above mentioned model shop quotes gauge wall thickness and their tube is spot on with enough metal to resist bending while it is installed, and then to be counter sunk for a smoother feel and improved looks.
It could be that 7/16 is slightly too big or too small, both a pain in the A...
