About a year ago, after some discussions, we decided to reject 'shaving myself'. Why? We believe that unless you're a barber, it's almost obvious that you shave yourself and not others and it's just a weird sentence in English because even English that loves specifying things (I put my hand into my pocket to reach for my phone) wouldn't do it here.
A little late to this party, but I see a difference between "shaving" and "shaving myself". "Shaving" I would use for my overnight beard growth, but, if I were a competitive swimmer, and removed the hairs on my chest and/or legs (for streamlining purposes, for example) then I'd be "shaving myself". It's not so much a reflexive, but "beard" vs "the rest of me".
Why no preposition? Is it instrumental case? Did we learn that? Did I miss it? I'm guessing from context and knowledge of Russian here.
EDIT: Yes, I see from Wiki that it is instrumental case. So, no preposition ever needed with the instrumental, as in Russian, right?
Some prepositions can connect with Instrumental but when you mean "with" in sense "using some tool" or you want to express using some instument/tool it is used without any preposition.
For example: "z" in sense "with" (accompanying) is used with Instrumental.
"Only" is a bit special. Although your answer is perfectly correct, for most native speakers the most natural position in spoken English for "only" is before the verb, whatever part of the sentence it applies to (apart from the subject).
Also, we wouldn't normally use "myself" here. With my English logic I might start wondering - If he only shaves himself with the green razor, who does he shave with the red one?
So what is wrong with my translation of...'I shave only with a green razor'? The word 'shaver' is unusual in English, tho' maybe a female shaver sounds less dramatic than a razor. Perchance the computer does not like my arrangement of words, but English is also quite variable. ( I am aware that Giletka might be a razor but I thought that both words meant razor/shaver. Ah, I see that SonofMaat ran into a similar problem. Apropos Jellei's comment, I have never come across such a distinction. You can shave yourself or anyone/thing else. It is just that, as I said, the instrument itself tends to be called a razor, unless we use 'shaver' as a diminutive-hence the expression 'just a young shaver-ie a young guy'. I remain, perplexed.
Shaver, to me (native UK English), is not an everyday word, but razor is. Also 'only' limits the word that follows. So ' I only shave' means that's all I do with it, I don't dig or cut or play with it. However, in speech, the majority of English speakers get this wrong. My translation was: I shave with only a green razor. I was marked wrong - I still think I was right.