I would doubt its possible without installing Google Play/Services.
I just tried Silk <puke> without any problems other than It doesn't allow you to take screenies. I did view as Desktop and bypassed m.youtube.com...
I don't have any problem wtith youtube.com either (wish there were a setting to have everything automatically in desktop view) but what fo you mean abt not being able to make screenies? In Silk, in general? On YouTube specifically?
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"Not everything that can be counted counts, and not everything that counts can be counted."- Albert Einstein (1879-1955)
I haven't been able to take a screenie, with my privacy settings/incognito mode (or whatever Silk calls it). I refuse to give it any more permissions and I immediately shut all settings for Silk down after testing.
I have used Silk TWICE in the past couple weeks just to test stuff out here on the forum. This was the second time. Don't believe I've used it since the very first time I tried it when I got my first Fire in 2016 - my HD8/6th Gen.
I just don't need it. I have Chrome, Firefox, and Firefox Focus on my two active Fires (HD8/6th Gen is a Digital Picture Frame now)...