What cream or lotion that will stop my hands from feeling really dry without that greasy feeling?

Cerave. Cerave, neutrogena norwegian hand creme are non - greasy hand creams that could be useful. You must also avoid irritating chemicals by wearing gloves during wet work. Allergy patch testing may reveal chemicals that you should avoid. This test is done by a dermatologist in 2office visits 2-3 days apart.
Moisturizer hands. Here's a very useful tip that works very well. Never use hot water, only warm, no antibacterial soap which can irritate the hand especially if someone has eczema. As soon as you've wiped your hands dry so that the skin is still slightly moist, immediately apply vaseline or aquaphor ointment. Rub it in and then take a tissue or paper towel and wipe the excess off your skin to leave a thin film.