江戸時代の後期から刀は銃に負けたって英語でなんて言うの？

To express that the use of the katana sword and the Samurai decreased as the Edo period started coming to an end with the introduction of guns, you may simply say;

Towards the end of the Edo period guns were introduced and katana swords became less popular. The number of Samurai also gradually decreased.
keywords:introduced-To bring something into effect.
to gradually decrease- To slowly become less.

It depends really if you are talking about the Samurai or the Katana swords. It would probably be better to make two sentences:one talking about the samurai and one talking about their swords.

This sentence is a cause and effect set up. "Due to" means because of and with that you explain the cause in the first part of the sentence. In the second part of the sentence, you can state the effect, which is that there were less katanas and samurai. English speakers know that katanas are swords so it is not necessary to say katana swords.

I hope that this helps :)

Dwindle' means 'to become fewer and fewer until there are nearly none.' 'Fewer' modifies count nouns. 'Less' modifies mass nouns. E.g.: Fewer cookies. Less water.

By the end of the Edo period, the distribution of guns affected the popularity of katanas, which resulted in the decline of samurais. - The sentence can be used to express that once guns became accessible to Japan, there were a lot fewer people using katanas, which resulted in a decline in the number of samurai.

When talking about a specific time (years) something happened then we call this a 'period' of time so you would say the 'Edo period' meaning that time
If something is used instead of something else then you say it was replaced
When there is not so much of something this you say it has decreased (gone down)

If you are wanting to state that katana swords were less popular after guns started being used, you can say "Once guns were introduced, katana swords became less popular."