Concern has been voiced about potential risks to privacy and data rights following agreement on a UK-Japan trade deal.
Alistair Carmichael has raised the issue during a debate on trade.
The isles MP has meanwhile welcomed continued protections for NOrthern Isles produce as part of the agreement.
However, he said a lack of clarity over future relations with the far larger European market would overshadow progress with Japan.
Speaking in the House, Mr Carmichael said: “It is significant that we have a deal with Japan: it is the world’s 11th biggest trading nation and our fourth biggest export market. It will be a matter of significant relief to the salmon farmers in my constituency for whom Japan is an important export market.
“It is also welcome that we have a continuation of Protected Geographic Indicators.
“The continued protection for Scotch whisky is supremely important for Scotland and I am delighted to see that. It is also important that we continue to have protection for Orkney beef, Orkney lamb, Shetland lamb, Shetland organic wool and Orkney cheddar.
“The protections given to those important local products are important, but it has to be said that Japan is not their biggest export market, so their producers will be looking for the successful conclusion of a deal with the EU sometime between now and the end of the year, because that market will matter to us.
“For example, for decades now Orkney cheddar producers have, at the encouragement of Governments of all colours, moved towards participation in that export market and produced a higher-quality product as a consequence.
“If they are now forced to compete on a different basis, and one for which tariffs will be payable, that will be a matter of great significance for them.
“The prospect of [personal] data being processed and somehow laundered for onward transmission—particularly to the United States of America, because Japan already has that agreement with the USA—should be a significant cause of concern for us all. I also venture to suggest that if that provision is to be left unamended, it will make it very difficult for us to do a future deal with the European Union.”