I do not know about these exercises. I know something (not-similar) that would work though https://www.dskeyboards.com/
....and don't overpractice finger-stretching. In a similar way Schumann got a serious tendosynovitis and hat to end his career as a virtuoso.
I have small hands too for a male and figured doing a lot of Rachmaninoff may help. He must have had huge hands. Can you actually play an octave with 1-3? If so i wouldn't be concerned very much. My teacher btw, can't, but she developed technique to play fast octave runs, legato, with 1-4 1-5.
Practice diminished and domintant 7ths holding all the notes down when you've pressed them. Do the same with Major 7th chords, do minor chords with major 7ths.Don't worry about hand size, I havn't really grown in the last 2 years, but my hands have. I have a 10th in RH, and an 11th (just) in LH. You'll find some pieces will help.
Well if you look at the hand, the thumb can stretch a very long way as nothing gets in the way.
A warm up exercise I use helps with both stretching and flexibility. Hands one octave apart starting on C in unison using RH 1-2-3-4-5 / LH 5-4-3-2-1 play the following pattern: C, C#,D, D#, E and back down D#, D, C#. Then repeat the pattern in whole step C, D, E, F#, G#, F#, E, D then repeat with a minor third between notes C, D#, F#, A, C, A, F#, D# then repeat with a major third between notes C, E, G#, C, E, C, G#, E and then instead of landing back on the C land on C# and start the whole group again until you have gone through all twelve notes of the chromatic scale. Everything is to be played legato with as much ease as possible. (Start slowly.)You can make the exercise really difficult by adding one last pattern to the group this time in fourths. (C, F, B-flat, E-flat, A-flat, E-flat, B-flat, F)