WASHINGTON (AP) _ Billy Henderson wasn't going to eat those hundreds of inaugural buttons, so ignoring the frigid weather, he was there on Monday: the only souvenir hawker working the parade-less, crowd-less presidential parade route.

And he did sell some, as a few families ventured from their hotels down to Pennsylvania Avenue and handed over $10, $15 or more for handfuls of buttons bearing the smiling faces of the president and wife Nancy, the president and George Bush, even the president and Elvis Presley.

But Henderson wasn't doing the business he thought he would be doing - ''a couple of thousand dollars,'' he estimated he might have had. And, multiplying that by the hundred or more other souvenir hawkers and food sellers who normally would have shown up to work a crowd of hundreds of thousands, the size of the loss begins to come into focus.

The second inauguration for President Reagan, champion of American business, was no bonanza for the small businessman in the nation's capital.

On a bigger scale, parade-route restaurants were also suffering and the area's subway system missed thousands of hoped-for fares. But the city saved money by simply not calling in hundreds of police officers who would have been brought in at extra pay, and the Metrorail transit system did the same.

There was no authoritative overall estimate of lost revenue, but there were some obvious things to look at. For example:

-The inaugural committee had sold about 25,000 bleacher seats along the parade route for a total of about $850,000. Organizers promised full refunds, but said they didn't know how many people would claim them, perhaps holding out hope that many wouldn't.

-President Reagan's two-story reviewing stand, built at a cost of more than $1 million, stood empty in front of the White House with only the wind whistling by instead of the expected bands.

-Two blocks from the White House, manager Hank Hemmendinger at the Old Ebbitt Grill said that ''with 400,000 people on our doorstep, we expected to be packed.'' The restaurant wasn't, but he said business was still not bad.

-Outside a bus along the parade route, Joe Wagner, accompanying the Brunswick (Ohio) High School Marching Blue Devils, said the trip to Washington had cost more than $30,000. Asked if it was worth it, even without the big parade, he answered quickly, ''Sure, look at the kids; they're thrilled.''

-Down the street, near the Capitol, Kenneth Lautner and his family waved as the president rode by on Pennsylvania Avenue - yes, he did ride by, parade or no parade - and then grinned to show that his return wave made their drive from Travers City, Mich., well worth the money.

-More than a quarter-million Washington-area federal workers got the day off, a theoretical loss of several hundred thousand dollars.

On a strictly business level, Susan Pepper of the Greater Washington Board of Trade said pre-inaugural estimates were that visitors would bring the city $30 million or more.

''You've still got the people here,'' she said, adding that ''all of a sudden people have a block of time'' - raising the prospect of frustrated parade-goers flocking into area stores.