Fine-fingered gets no hits on Onelook (which searches dozens of dictionaries), and this suggests its usage is limited in English, although Wordnik includes it and defines it as
Delicate in workmanship; expert at fine work.
This can apply to many things, but not necessarily the activities you list. One doesn't have to be fine-fingered to make the bed or wash the dishes. It applies to activities of a more intricate nature, such as needlecraft or sculpting small, detailed objects out of wood or ivory.
Someone, whether male or female, can be called a homemaker, so you can say 'He (or she) is a good homemaker'. One's skill in activities that involve the hand, whether they are sewing and cooking or hunting and gardening, can be described as handy (see especially definition 3).
The ideal God-fearing woman is described in Proverbs 31:10-31, and shows such a person (it can also apply to males) as industrious in important tasks & responsibilities outside of the home:
A good woman is hard to find,
and worth far more than diamonds.
Her husband trusts her without reserve,
and never has reason to regret it.
Never spiteful, she treats him generously
all her life long.
She shops around for the best yarns and cottons,
and enjoys knitting and sewing.
She’s like a trading ship that sails to faraway places
and brings back exotic surprises.
She’s up before dawn, preparing breakfast
for her family and organizing her day.
She looks over a field and buys it,
then, with money she’s put aside, plants a garden.
First thing in the morning, she dresses for work,
rolls up her sleeves, eager to get started.
She senses the worth of her work,
is in no hurry to call it quits for the day.
She’s skilled in the crafts of home and hearth,
diligent in homemaking.
She’s quick to assist anyone in need,
reaches out to help the poor.
She doesn’t worry about her family when it snows;
their winter clothes are all mended and ready to wear.
She makes her own clothing,
and dresses in colorful linens and silks.
Her husband is greatly respected
when he deliberates with the city fathers.
She designs gowns and sells them,
brings the sweaters she knits to the dress shops.
Her clothes are well-made and elegant,
and she always faces tomorrow with a smile.
When she speaks she has something worthwhile to say,
and she always says it kindly.
She keeps an eye on everyone in her household,
and keeps them all busy and productive.
Her children respect and bless her;
her husband joins in with words of praise:
“Many women have done wonderful things,
but you’ve outclassed them all!”
Charm can mislead and beauty soon fades.
The woman to be admired and praised
is the woman who lives in the Fear-of-God.
Give her everything she deserves!
Festoon her life with praises!
Thus, "a good woman" was not confined within the house in ancient Israel, although in some cultures they are even today.