Merriam-Webster's Eleventh Collegiate Dictionary (2003) offers three definitions for sketchy:
sketchy adj (1805) 1 : of the nature of sketch : roughly outlined 2 : wanting in completeness, clearness, or or substance : SLIGHT, SUPERFICIAL {the detail are sketchy} 3 : QUESTIONABLE, IFFY {got into a sketchy situation} {a sketchy character}
The sense of "iffy, questionable, ambiguous, or not yet settled" implicit in definition 3 above seems to have morphed at some point into the sense of "unstable, unreliable, or dangerous." To me, the shift seems not especially surprising—just as the shift from "roughly drawn or outlined" to "incomplete or not filled in" and thence to "questionable, iffy" follows an intuitive progression.
A Google Books search turns up several matches for "sketchy neighborhood" and "sketchy area" from the 1990s. From The Princeton Review Student Access Guide to America's Top 100 Internships (1993):
Quality of Life
Creative environment
Workshops and Evert lectures; Sketchy neighborhood
From Elisabeth Scribner, Italy '96: On the Loose, On the Cheap, Off the Beaten Path (1995):
The main drawback is the sketchy neighborhood; women might not want to wander around alone at night.
From Jeff Brauer, Julian Smith & Veronica Wiles, On Your Own in El Salvador (1995):
Mail: The central post office is in a sketchy area just north of the Centro Gobierno, east of the Parque Infantfl and the Palacio de los Deportes.
From The Right to Live Without Violence: Women's Proposals and Action (1996):
The explanation, apparently, is that when a girl is raped on the corner of some sketchy neighborhood, she tends to say, "I'll never go back to that place, I'll just stay home." But if she is raped at work or in her house, she has no safe place left where she can seek refuge, where she can escape.
From Central America: On the Loose, on the Cheap, Off the Beaten Path (1996):
This is a sketchy area—take a taxi.
From Shaheena Ahmad, The Yale Daily News Guide to Succeeding in College (1997):
It's also not a good idea to take a job too far from campus; you don't want to be paying an arm and a leg in transportation costs or losing an arm or a leg after walking home from work through a sketchy neighborhood.
From Frommer's San Francisco from $60 a Day (1997):
The only drawback is the sketchy neighborhood, where there's a lot of hustling for change going on, but that's life in the Haight.
It thus appears that sketchy in the sense of "unsafe" was in use in the United States by 1993 and proliferated during the mid-1990s.