Well either your garden is ok or it is not - it can't be ok by day and not at night.
If you know that you get foxes in your garden regularly then I think you'd have more of a problem - I have heard of dogs catching things from fox urine - but I've never heard of a dog catching anything from a cat or a squirrel other than fleas/worms which are always a possibility. However I may be wrong, and if so then I'm sure someone will correct me!
I wouldn't put him on a puppy pad by the door - you are teaching him that it is ok to wee in the house. I would take him outside, across the patio and straight to the grass, put him down at the edge. Puppy lead can be a good idea so he cannot run off into the exciting dark garden - but I would expect he will stay close to you. And remember to use your cue word (we say, hurry up) plus praise when he goes, but just quietly.
(Also remember to keep an umbrella by the back door, very useful!)