Drilling / pocketing with small straight bits

Hello,
The smallest bit I have is a 1/16" straight bit. I need to drill holes as small as possible. Would it be safe to pocket cut a 2mm circle using this bit? I’m unsure because it does not have a cutter in the center. I even checked Drilling Process Video for help ,but it did not help much.Any advice on how to do this with a 1/4" shank? I’d happily buy a proper drilling bit, even if smaller than 2mm. But with a 1/4" shank there doesn’t seem to be many options.
Perhaps the drill press is the best method. I just have a lot of them to do!

Any help will be appreciated.
Thank you.

Here is an excellent video that will answer all your questions:

https://m.youtube.com/watch?v=dQw4w9WgXcQ
.

Just buy a 2mm bit and a mini drill chuck off amazon total cost <20. If you try to use a 1/16 bit and cut in plane it won’t be accurate and will break.

What are you drilling? Without some sort of drill press/guid if it’s metal it’s not going to be fun.

Not sure what you mean by “pocket cut”. Do you need to counter-bore, as with a Forstner bit? Or are you making a pocket-hole for a screw, as with pocket-hole jig?

Perhaps one of the Kreg jigs would be helpful.