Low Profile Tyre Recommendation

I don't know why you're not just using some non-euclidean geometry to make the tyre fit.

The reason bike companies don't give the profile height is because it is entirely dependent on the rim width and bead seating. I'd suggest you try a 23mm, or look around specialty tyre sites for smaller. In the 80's we raced on 19mm tyres, but they were tubulars.

ALternatively you could find a wider rim which will mean your tyre sits lower. Also you could try other brands of tyre, as not all tyre dimensions are created equal.

I think I had got a 20mm tyre for my peugeot racer in the late 80s early 90s.

Oh Great Dead Lord, rest assurred that a swarm of drowned Tsothoggians are painfully transporting a precious 18mm tyre through the deepest rocks for your great commute.

What size were the original tyres?

21mm! Luxury. I bought a second hand  steel framed Italian bike for my daughter to try out and it came with 20mm tyres. I will check with a bike shop or two what most riders are using on road bikes these days because last time I asked (2017) 23mm was the most common choice.

Aaah, a bike made for really skinny tyres; brings back memories, that does.  In those far off days 21 or 23mm were the tyres to be seen on, but now we know different and 25 is the absolute minimum any self-respecting rider would suffer.  And it looks as though 28 is about to take over at the top of the Christmas lists; where next you may well ask.

But, back to your problem.  There's nothing wrong with the Zaffiro, it's good value, but even better if it doesn't rub the paint off your fork.  You could try a 23mm, I guess it will fit, but it's only a guess.  Failing that, ask your LBS for guidance, they often know stuff like this.

And you can keep the useless 25mm until it replaces the one you wear out on the back of the bike.

Best of luck.