For field work we used to use roughing taps (smaller on diameter, same pitch) for this type of work.
Say for 1.25-7, the first tap would be 1.18-7, the next 1.23-7, then finish tap was size or even +.002 to .003 depending on where we were and what the threads were meant for.
If for thru holes a very long lead on the tap can be advantageous.
Edit: I missed these were blind!, use a heavily tapered tap first anyways, unless you go with the roughing taps like I mentioned earlier.
We'd also usually go 1.125 to 1.133 for minor dia. You can "feel" the difference between that and the actual tap drill size When hand tapping. If your over 2x dia, or in steel, depending on application should be more than plenty good % thread wise. Hell we did that on steam turbines, steel mill parts, etc stuff under heavy load even.
Good luck, when I was an apprentice I had to do all kinds of hand tapping of 1"+ threads. Drink lots of water and work steady, and stay safe.