We have WIFI at home thru Cable, but on the road we have Verizon and T-Mobile - and unlimited data, so should be fine - Like you said, just let it load and watch it later.
One thing tho', I looked at Firestick, and it says "Just tell Alexa" and it starts. We have NO Alexa, and have no interest in it. All we want is ability to watch some movies on the road. We don't want satellite either. We're just looking for convenience of a movie or series occasionally in the evening.
So, just because it says on the newest Firesticks: 'Tell Alexa to start', does that mean it only works if you have Alexa ... makes little sense, but technology sometimes inhibits the very thing it enhances.