First, you've mentioned two separate Roku devices: Premiere and Streaming Stick. Which you have doesn't really impact the answer, but the mentioning of two separate devices as one device makes me wonder if you're actually asking something else other than what I'm reading.
Ignoring that, I'm reading that you have a device plugged in to the single HDMI port on your TV, and want to use another device in that same port without having to plug/unplug cables every time.
You call this non-Roku device "the box," which I assume means cable box, although it could mean anything. Clarifying what "the box" is might help. If it's an Xbox, you'll want to keep that. If it's a cable box, you have the option that so many others here have chosen: stop using it. More in a minute.
For now, you can get an HDMI switch for around $20 or less from Amazon, Best Buy, etc. The catch is, you'll want one that you manually switch, not one that automatically switches. The automatic switch can suddenly switch inputs if it detects a signal on the device that's not in use. And yes, that can happen. So, you'll likely want to manually switch to prevent that, or be prepared to have to manually override an automatic switch.
Another option is a new TV. A single HDMI port is very uncommon, meaning that might be a much older TV. A new TV is a larger expense -- around $100 or more depending on the size -- and unless you have the need or strong desire to get another TV, that might not be the way you want to go.
And, another option is get rid of "the box," assuming that's a cable box. If you are a Comcast/Xfinity customer, you can use a Roku as the cable box. I've done that and family members have done that. It's a little bit to get used to, but it does work.
Other cable services may also have an app that will allow this; my only personal experience is with Comcast/Xfinity. You may wish to look into that. If that's an option, you may find you can turn in "the box" and save money.
Another option for getting rid of "the box" -- again assuming it's a cable box -- is to drop cable. There are live streaming services that offer content. Essentially, you'd keep your Internet service and replace the cable service with a live streaming service. The cost varies on those. You can go to https://suppose.tv and enter your location (city/ZIP is sufficient) and pick the must-have channels you get from cable. Select Roku (or any device, really) as your Device. It will let you know the live streaming options and approximate monthly cost.
DBDukes
Roku Community Streaming Expert
Note: I am not a Roku employee.
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