John915 has essentially covered it The practical application of his second sentence is to use the NA search facility,
http://discovery.nationalarchives.gov.uk/Leaving out any short cuts, entering James W Muir's name first brings up 320 records. Limiting the dates to 1900-1924 and refining the search gives 261. Now go to advanced search and enter WO in the bottom references box (WO gives army only results). That gives 4 results only one of which is a Royal Engineer (and just happens to be your man) and it is his medal card. Clicking on the title will give a page that says you can go to Kew and see it free, download it for £3.50 or find it on Ancestry (FindMyPast have only the transcrpiton) if you have a sub. Now try WO 363 and WO 364 in the reference box, answer zilch.
If there had been a record burnt or unburnt for him, it would have been listed there.
Just to prove it, enter Arthur Heath and WO 363 and you will see his record has survived. Clicking on the title shows you can see it on Findmypast and Ancestry (check "other ways") and view free at Kew.
Broadly speaking army records that survive are to be found at Kew and also on the two subscription "Partner" sites. When I have advised that only James Muir's medal card exists, I have done that from checking those sources.
As john915 also hints, there are other records from which, with practice, one can get clues. On Findmypast this link shows all the British Army records they have.
https://search.findmypast.co.uk/historical-records?SearchedRecordsetName=british+army&Region=united+kingdom&subcountry=&subcountryfieldname=If you click on any of them and scroll down to "discover more about.." and "available record series" there is an explanation of where all the originals came from which in the vast majority of cases is the National Archives.
The process isn't totally straightforward but no research is. If all else fails, do as you did earlier and post his name. I, and I'm sure other who have posted here, will tell you if a record does or doesn't exist and will tell you if they aren't sure.
MaxD