Draga Sergiu
Dont change the coticule (it is the ideal size)
Send the TI to someone who knows honing
Buy a second razor to learn honing knowing from the first, how sharp must be a straight razor.
Hone the second razor, test shave,
dull it with different methods(corc, match, writing chalk, one pass,two pases etc), hone it, test shave, dull it, hone it, test shave etc. , etc until you feel that the results are not luckily and you are confident that you have the possibility to produce a fine edge if a razor is dulled.
Probably for this, you need and a coarser stone.

Bun noroc si bune rasaturii (if I remember well Limba Romana after 25 years...)