We have an eleven year old rescue greyhound called troy, and a nine year old overweight rescue lurched called gyp who has recently gone blind.
We work full time, however different shifts so they are usually only home alone four or five hours. They do longer occasionally but I wouldn't do it every day.
Troy refuses to go out for walks if it is cold, wet, windy or dark, and sometimes just because he would rather stay on the sofa. Gyp will go out at any opportunity but has to be talked to the whole time so she knows where you are, leading to people referring to me as the mad dog lady

Neither shows any interest in cats rats or mice and gyp actually ran away from a deer that jumped out near her before her sight went despite having been bred to work them. She is a deerhound x

They really are worse than toddlers, and I had gyp from a pup so can't blame anyone else. Having said this, I think rescues are the best in the world.
I know our local RGT are always very helpful, if you like Greys why not ring and talk to them?