Lacking a grater is there any tips or tricks to make little cheese particles other than slicing thin strips off with a knife and chopping?
I’d like to help, but I’ve always had a grater. I wanted shredded cheddar the other day, but I’d just washed my grater and was lazy and didn’t want to wash it again; so I just did the slice-and-chop. Being hard and crumbly, Romano will probably be quicker and easier.
OK, so I’m not any help. But I have one of these. For hard cheeses like Romano or Parmesan it’s just the thing. This particular one has a very short ‘funnel’ thing that falls off easily, so I don’t use the ‘funnel’ ring. But the grater itself makes quick work of a slice or block of hard cheese.
But for now? Um… Do you have a rasp in your tool box you can wash? 
Use a serrated knife and scrape it up and down the cheese. Not perfect, but it does the job in an emergency.
That’s what I’ve done from time to time, using a serrated steak knife. It works ok. Hold the serrated blade perpendicular to the block. You should get lots of little shavings.
I heart my Zyliss grater. I’m gonna start bringing mine when I go to the Olive Garden, and just tell the server to leave the wedge.
A hard cheese might work well with a veggie peeler.
Are you going for a large quantity? If you have a food processor, you can use that. Chop the Romano into half inch cubes, then use the swirling blade at the bottom of the bowl, not the shredding disk.
You could just shave it with a Stilleto or an Opinel. Thin, long, shavings… wield the wedge as an arrowhead, whittling down.
If you want to be authentic.
Or a vegetable parer, such as you might use for peeling potatoes or carrots. There are worse ways for your Romano to land on your food than in thin, slightly curled sheets (such as in little clumps poured from a green cardboard can).
If you have a mortar and pestle, you can crumble bits of it, broken off. Due to the nature of the cheese’s intrinsic structure you should get a fine product with enough grindage.
Do you own a Ped Egg?
You know, that was the first thing I thought of and almost posted it! 
How about a rasp from the toolbox?
Just remember to empty and wash the compartment first…
“Cheese or foot callus? Hmmm…”
I have used my lemon zester for a small amount of shavings when I was in a hurry and didn’t want to dig a grater out of the cabinet.
I think I would go for my coffee grinder, which is really my spice grinder. There has never been a coffee bean in it. $10.
The veg peeler recommendations are spot-on. You may find that you prefer the little shards and curls of cheese it creates over the texture of grated cheese. I know that I like the “shards” in a caesar salad best.
That was my first thought. Or a rotary rasp on a drill.