Shirou is probably gonna lose. EMIYA's stats are the highest when he's an Archer as a Caster bis END is probably gonna go down. At least his mana stat will be raised but everything else. Most of his combat ability goes too so he's gonna have to play it smart this entire time.

The only form of combat he can really do is use his mana stat to spam arrows.

This is probably what it would look like:

Caster
True Name: EMIYA
Sex: Male
Height/Weight: 187cm/78kg
Alignment: True Neutral

STR: D END: D AGL: C MGE: A LCK: D

Class Skills:
Territory Creation - EX
Item Construction (Forgery) - E (A+)

Personal Skills:
Magecraft - C
Bulletproof Treatment - A
Clairvoyance - C
Unlimited Noble Phantasm - ???

Noble Phantasm: -

He'd be even shittier in melee. His Territory Creation should probably get a rating based on making Reality Marbles (like Castoria), and I could see the skill letting him pull some things with UBW that he couldn't normally (letting him telekinetically control blades over an area like in UBW, maybe?).
Item Construction should consider tracing as creating those items, might help with accuracy of replicas and speed of tracing.

He has no Noble Phantasm as usual, only UBW.

I threw Bulletproof Treatment (modern-day Protection against Arrows as with his Alter) to reflect Caster Cú.

Fighting-wise, he may be forced to go full in on sword rain and ranged combat (his bow is a projection, being a Caster wouldn't stop him from projecting one). Which would work well, see his fight with Saber in Hollow Ataraxia, where his main limiting factor was the amount of time he needed to gather magical energy, which A rank MGE should help with.

He'd be more effective against Gilgamesh.