DCon is effective, but often the mice go elsewhere to die. If it is in your wall or other inaccessible place, you have a stinky situation for a week or so. We use old-fashioned snap traps, baited with peanut butter (not cheese.) Then you know where the body is…and can dispose of it cleanly. You can disinfect the trap and reuse.
I have had cats in my past life, and some of them are extremely lazy. Others are avid hunters. Depends on the individual cat. Don’t care for them since they tend to poop in my nice clean garden…and elsewhere. Will not tolerate kitty litter in the house. Can pick up diseases from them too… OK now some of you hate me