Khandro:
When you try to access BBC iPlayer, Auntie Beeb's servers examine the IP address that your request is coming from. That's allocated to your home router by your internet provider and will be exactly the same whether you're using a smart TV, a computer, a Now TV stick or anything else which gets its data through your router. So using a Now TV stick wouldn't enable you to bypass the restrictions that the BBC is legally required to put in place regarding access to iPlayer from overseas. [You'd also find it difficult to sign up to Now TV anyway, as Sky (who own Now TV) doesn't hold the overseas rights to the programming it transmits].
The only way that you can access geographically-restricted BBC content from overseas is by using a VPN, which routes your internet traffic via a UK-based proxy server, so that the Beeb's servers 'see' the IP address of that server, rather than the one allocated to your home router. If you go down that route, it would be best to use a VPN that has multiple servers in the UK. Then, if the Beeb blocked access from one IP address used by your VPN, you could simply switch to another one.
Using a VPN on a computer is very easy. You simply install the app and away you go in just a couple of clicks.
Using a VPN with a smart TV that uses the Android operating system is fairly straightforward too; you simply need to download the VPN app and configure it.
However most smart TVs aren't Android-based, so things get a little (but not a lot) more complicated. You can go into your router's settings and make changes there, so that all internet-enabled devices in your home send their traffic through the VPN. However that method can be a little daunting for people who aren't 'technically-minded'. It's far simpler to set up a wireless hotspot from your computer. (The only downside to that is that you'd need to have your computer turned on whenever you were accessing BBC iPlayer on your telly).
In your position, my own choice would be to use Nord VPN. They've got plenty of UK-based proxy servers and offer high-speed connections (so that you don't end up with a lot of 'buffering', as you can with slower VPN services):
https://nordvpn.com/
(When you go to that page, you'll see an offer that expires in 9 hours 39 minutes and 40 seconds. Everyone always does!)
The 'Help' section of the NordVPN website is particularly good. For example, click 'Help' (at the top right of the screen) and type 'smart TV' into the search field. Scroll down to 'Sharing a wireless VPN connection from your Windows PC' and click on it to see how to turn your computer into a wi-fi hotspot.