Below is the list of the twenty highest WHIP's put up by relievers appearing in 40+ games, since 1901. I'm defining a reliever as a pitcher making 80% or more of his appearances in relief so a few swingmen may show up on the list.
Highest WHIP in a Season by a Reliever in 40+ Appearances
The only pitcher with a decent FIP is Tony Fossas, but I'm almost positive that's because he was a LOOGY (Lefty One-Out GuY) by that time, although the fact he only gave up one home run didn't hurt. Dick Welteroth has one of the worst K:BB ratios I've seen, striking out 37 strikeouts while walking 89 batters. It may not entirely be his fault; the American League as a whole put up one of the worst K:BB ratios as a league in their history in 1949.
To wit, here's a chart I quickly put together using the total bases on balls and strikeouts for each season available on Baseball-Reference.com (click to enlarge the image in a new tab/window):
Not only is it evident the AL in 1949 saw more walks relative to strikeouts, you can also see the pitching-dominant year of 1968 in the chart as well, in climax of the upswing following 1949. Pretty crazy stuff going on in the junior circuit.