welcome to the forum.
do you have any experience of finishes, stains and matching stains ??
how about tools for applying finishes.
one of the tools that is available is a "color wheel" to match stains.
on small jobs, once the desired color is achieved, I would apply it with an
artist's airbrush. of course this is a bit advanced for the average person.
a foam brush, cloth or regular brush can be used after much practice.
or - if this piece means a lot to you and you want it done right, hire a
professional to do it for you.
Note: the stain on your cabinets could be oil based, water based, transtint dye,
or any number of proprietary stain/finish that a commercial shop would use.
matching what you have will be a challenge.