If you're travelling for business outside of the UK then there will not likely be any UK VAT on the purchases that you make whilst in these countries.
You are only able to claim back UK VAT which is charged to the company. Any non-UK VAT would be a sunk costs you are unable to reclaim.
With any VAT purchase, it is always worth checking your receipt as to what VAT has been charged to your business.
Which VAT rate to use
For expenses that are made outside the UK, and do not include UK VAT, the most appropriate category would be No VAT.
Do these expenses still reduce my profit for tax purposes?
If the expenses are a valid business expense, which is not specifically disallowed*, then it will still reduce your profit for tax purposes.
*for example client entertaining. For more information, please click the information icon next to the category chosen in Ember