It's possible to get odorless spraypaint (or, rather, what is marketed as odorless spraypaint), but even then I wouldn't be comfortable using it in an enclosed, poorly-ventilated space.
I especially wouldn't want to be one of the actors huffing that paint at every single performance in said enclosed, poorly-ventilated space.
I can think of some alternatives, but they tend to fall into two categories:
Tech-Heavy and/or Esoteric
- Instead of spraypaint, give them cans of spray mist. As they begin misting (pretending to spraypaint), jam a fogger to full-blast and let it run until the whole stage is covered. As the stage is covered, slip on-stage and somehow modify the set piece (flip it over, spin it around, affix a new front, whatever), then clear the stage before the fog clears. Augment with rockstar lights and headbang as required.
- Get some thermochromic paint and cans of aerosol water. Paint the surface, doctor the aerosol water so the cans look like spraypaint, and get off to the races. The sprayed water should produce a sufficient temperature differential to get the thermochromic reaction going. It'll only last for a few seconds (we're talking 30-60 absolute, if-you're-very-very-lucky most), and the water will react very differently to spraypaint, but it will still basically look like your actors are spray painting, even though they aren't. (This effect would be significantly more pronounced if you can talk your director into letting you use a roller or a brush, in that you can use substances other than water (which will behave more like paint--although you'll still want water-soluble stuff for easy cleanup) and you can better control the temperature of the substance, which will produce a more visible (and longer-lived) thermochromic reaction. A roller thoroughly doused in ice water applied to a thermochromic surface which has spent the last hour grilling under stage lights would give you a very pronounced effect. A quick spray of aerosol water which is essentially at ordinary room temperature, not so much.
Cheap and Cornball
- Invisible UV paint. Pre-paint the surface with the UV paint, give your actors cans of something inoffensive (hairspray?), then flick on a blacklight as they start painting and the graffiti magically appears. Pray nobody in the audience is reminded of county-fair haunted houses and/or early 1990s Batman movies.
- Gobo. When they start painting, turn it on. Then redo all of your blocking so that nobody ever crosses the beam, lest the graffiti migrate to their face.
- Utterly cheat it: have the wall visibly flip, or have the actors affix something to the wall, or do whatever else as they paint it.
I'm mostly being silly. What I will say, though: if you can't find some way of doing this without spraypaint, I would strongly encourage you to take this up with your director as a potential safety issue. Wafting odors into your audience is a bad idea, but making your actors essentially huff paint every performance is an even worse one.