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While some people run LT tires, an ST tire is what is really called for for trailer service. There are several threads (use the search engine) where those who propose the use of LT (light truck) tires state their case. Some of the arguments are valid, others seem questionable.
On the rims - even though the Chevy 6 holer might fit, there are several reasons not to use them. Your trailer requires a "0" offset wheel, some of the Chevy rims have a marginally too small center hole to fit the Airstream hub, and, most importantly, the weight rating of the rim must fit the weight requirements of the trailer. Trailer requirements are generally more severe (must have a higher weight rating) than the "regular" truck rim can deliver.
Rims from just about any vendor (trailer specific internet sales houses are usually the cheapest) will work, just be careful that the size, offset, and weight ratings meet the original specs.
"Suck it up, spend the bucks, do it right the first time."
WBCCI # 1113
Trailer '78 31' Sovereign
Living Large at an Airstream Park on the Largest Lake Totally Contained in Texas
Texas Airstream Harbor, Inc.