This response is based on the information provided.  We suggest you discuss with your contracting and finance team, program manager and/or legal department as appropriate. 
 
The contractor's assertion that " there is no such thing as an allowable or unallowable tradeshow/airshow" is not incorrect.  What is allowable or unallowable are the costs of participating in a given airshow.  We do not believe that FAR 31.205-43 really pertains to tradeshows/airshows.  FAR 31.205-38 applies to the extent that it refers back to FAR 31.205-1. But tradeshows and direct selling are different.  The nature of tradeshows is broad and not targeted to a specific potential customer.  While direct selling may come from contacts made at a tradeshow, tradeshows on their face do not constitute direct selling.  FAR 31.205-1 does allow costs of tradeshows, subject to specific limitations identified in FAR 31.205-1(d)(2), if the contractor can make a case that its participation in the tradeshow is driven toward the promotion of exporting its products/services from the United States. 
The second question you pose is not a FAR/DFARS question.  This is a judgment call.  Although subjective, you should apply certain objective considerations.  These considerations might be the overall nature of the event.  Is the targeted audience primarily foreign nations/companies?  IS the nature of the event heavily social or heavily technical?  What personnel is the company sending; more technical or more business development/sales?