Give Bernie Wright a call if you have any trouble placing him in a rescue - she's a rescuer and animal rights activist in Dublin and she will help or put you on to those who can. She should be on 0872651720 or email: [email protected]
Bernie is fantastic, a complete star. :)
I'm in England but used to get dogs out of Irish pounds and into English rescue... sadly your stray dog situation and put to sleep rate is even worse than ours and ours is pretty crap. I wouldn't hand ANY dog to the pound in Ireland personally. The place you said will kill him in 5 days if not claimed is almost certainly a council pound - strays have just 5 days over there and are killed in HUGE numbers (in England our pounds must keep the dog for 7 days).
What you will need to do is advertise him as found (better to be vague and say "found, small grey and white dog", than, "found, Shi Tzu", as you don't want undesirables claiming he is theirs unlawfully and harming him). IME the problem in Ireland is abandoned dogs just as much as missing ones, so it's possible, particularly given the state you say he's in and the breed, that he's an abandoned (or even escaped) ex puppy farm stud.
I personally would wait a bit before bathing him, to allow him to settle. As for a wee, take him into the garden on a makeshift collar and lead (trouser belt!) or better still pilfer one from a dog owning neighbour for a couple of days. Do so after he eats - he may well go to the door to tell you he needs a wee, though if he appears unhousetrained that is yet more indication that he's been puppy farmed.
If I were you I'd contact Bernie on that number above to see what she advises re the laws in Ireland with respect to caring for a dog you have found (and how to get round approach unkind, unhelpful regulations!). I know what they are in the UK but of course you don't share our Parliament. If you can't reach Bernie then please let me know and I will find you somewhere else.
Lastly, bless ya... so many folk would leave the poor boy out in the cold, what a lovely person you are.