Word that means "almost collide with me"

"The red guy approached me." (No contact/motive unclear)

"The red guy engaged me." (No contact/menacing implied)

Graze

ɡreɪz/

verb

touch or scrape lightly in passing. "his hands just grazed hers" synonyms: touch, touch lightly, brush, brush against, rub lightly, shave, skim, kiss, caress, sweep, scrape, glance off, clip "his shot grazed the far post"

Near miss

noun

1. a narrowly avoided collision or other accident.

"she had a near miss when her horse was nearly sucked into a dyke" synonyms: close thing, near thing, narrow escape, close call, nasty moment;

You could say brush past:-

to push quickly past someone or something. She brushed by the little group of people standing there talking. I brushed by the plant, knocking it over.

Then your sentence would read "He brushed past me".