I would try what you have in a similar piece of scrap, see what happens. 3.7mm seems on paper too small but it might drill oversize and be just right. Obviously don't over stress the tap if it doesn't want to go, but assuming a non-safety related attachment then there is a fair range of tolerance.

To; Andrew, without checking your figures but accepting, I agree and for most purposes 60% or so is adequate.

OP, vic, always go for % engagement. Your query relates to a small diameter tap which therefore lacks torsional strength. Dont push your luck with say 90/95% or you could snap it, especially a carbon one and small diameter as well.

A good example of what I think are often dodgy charts is where brass thread taps are shown as needing a 64th inch diameter drill less than the nominal tap size.When you use larger diameter taps, it becomes very obvious how much torque is needed to turn the wrench. Electric motor driven threaders are used on large-ish diameter pipes, e.g.

If it don't want to go, don't force it. I have tried a drill and found the HSS tap starting to twist so I took tap out and consulted my drill sizes charts to use the very next larger and it went OK.

My "bible" for all this is Tubal Cain' s "Drills Taps and Dies" (Workshop Practice Series No. 12). All the drill sizes for various engagements for every thread system you are likely to need. Suggest copying and laminating, for workshop use, the charts you need.

Worth a read from cover-to-cover.