I dug out 'Manx Traditional Furniture' by B.D. Cotton pp 286 profusely ilustrated ISBN 0-901106-34-8 1993 published by and based upon the extensive collection of Manx National Heritage (Manx Museum etc) - no such 3 legged table with feet is mentioned, nor is the name 'Manx table' even mentioned though they do say they were known as 'snap' tables (from a card game I think) and were apparently imported though there are recorded cabinet makers in Douglas from early 19th C so some may be local copies - there are many three-legged tables, those with known or likely Manx provenance are sturdy rustic designs usually in pine but usually dating from early 19th - they note 'this style of table which was made by manx joiners is closely similar to those made in other parts of the British Isles . However no 17th or 18th century examples have been recorded on the Island to date (1992). This is surprising since round topped tables with 3 legs were made elsewhere in Britain from 17th C...'
The traditional Manx table was a large 4 legged square top - many accounts of such tables in farmhouses survive.

As I said the 3 legs were well known as the Manx device (you will find a reference in Shakespeare) thus the connection.

Shoe/boot making was common but it was everywhere as shoes were generally made to fit individual feet - there was no export of Manx shoes etc noted (until the 20th century Ronaldsway shoe company opened up) in fact the exports were usually of hides so not even an extensive leather trade.

All commentators note the absence of trees (the current forrests have been planted within living memory) and in many parishes trees are very rare (eg in Kirk Michael )