I don't think that there would be an advantage at all.

All the major banks announced that they were going to phase out cheques with an end date of two years ago. It was only a massive protest by the charities and the senior customers that prevented it happening. Grudgingly the banks continued to issue cheques, but only if requested. The downside is that the recipient has to pay a charge to get it cashed. Most charities have moved over to plastic (credit/debit cards) for that reason.

The only places that accept Traveller's Checks (apart from large and expensive hotels), are banks or Bureau de Change offices, but as you are there, you might as well use plastic.

As an aside, don't forget that you will be exempt from VAT (20%) on goods (the kilt you buy), but not on services (the breakfast you ate before hand).