I'm sure others will have suggestions for you but if your maternal ancestry, as far as your paper trail goes, is centered on one area, the UK for example, and your DNA results give you matches with people with Asian ancestry then your assumption may be correct. I don't know how popular DNA tests are in Japan (if you suspect that might be where the father hailed from) - probably not a great uptake I am guessing.
You may match with Americans with Japanese ancestry which would give you some indication.
If you took an autosomal test, it would give results for both the maternal and paternal sides of your family. It can be a challenge to work out which match belongs to which side.
Is your mother still alive? If you also asked her, or one of her siblings, to take the test too, you could eliminate those matches you have in common, in theory just leaving the matches on your paternal side.
A lot of people are testing with Ancestry (I tested with FTDNA) but there are other companies as well. I think your timing might be a bit unfortunate as sales are just finishing or have already finished. (I know FTDNA's test was $39 but it finished yesterday
). A lot of people on rootschat have taken tests with Ancestry so will be able to advise you further.
Sales do come round every now and then, but presumably there will be delays in getting results due to increased sales.
You have nothing to lose.