Hi endlercollector and welcome to Everything Aquatic!
In my experience, generally it is tanks UNDER 10 gallons that finding a way made level one capable UV Sterilizer that will fit is a challenge.
However since your tanks are 10 gallons and above this should not be too difficult.
As an example I have a small 14 gallon aquarium with a 7 watt SunSun UV Sterilizer.
The problem is not that you need as small a UV as you noted, rather that the HOB filter you have currently running cannot run a UV Sterilizer so you will need either a separate additional power head/water pump/filter or an internal submersible UV, of which most are not level one capable
As for UV size, and as per
UV Sterilization; Facts & Information, turnover will hardly be a problem since 1.5 times per hour is the minimum, as it can be higher.
So for a 10 gallon the minimum is 15 gph and the 20 gallon aquarium is 30 gph minimum.
Flow rate is probably the most important controllable factor, which means a high dwell time Vecton 8 watt, which requires a maximum of 35 gph per watt, could go as high as 280 gph, BUT it can be much slower too. You simply get even more effective UV Sterilization
Other considerations beside the flow and turnover rate:
*Low water turbidity (pre-filtration takes care of this)
*A water temperature between 20 C (68 F) and 40 C (104 F)
*A gap of 3 mm or less between the bulb or quartz sleeve and the wall of the unit
*A GOOD water flow pattern inside the aquarium. or pond.
*A clean Quartz sleeve/lamp
*A hot cathode Low Pressure UV bulb/lamp with less than 6 months continuous use (NOT an old or cheap medium pressure UV bulb now so often sold on the Internet for $10 or less!!)
If a medium pressure bulb is used (commonly sold at discounters), you will need divide the maximum flow rate by 1/3.
With the before mentioned SunSun 7 Watt UV, these are best at a maximum of 25 gph per watt, so 175 gph is the highest flow rate (but again lower is OK too)
The other option is the submersible, such as the SunSun CUP-609 9 watt UV. This has an adjusted flow rate of about 160 gph, which is fine for a 9 Watt UV Sterilizer (max would be 225 gph)
If you were to use a standard inline UV such as the Sunsun/Terminator or the Vecton (the best), you would need to connect it with other parts as noted earlier.
The pictures below show a few ways to connect (further information is found in the product and information resources I will provide at the end of this forum post)
Please click to enlargeProduct Resources:
www.americanaquariumproducts.com/InternalUVSterilizer.htmlwww.americanaquariumproducts.com/CompactUVSterilizer.htmlwww.americanaquariumproducts.com/TMCUVSterilizer.htmlwww.americanaquariumproducts.com/AquariumUVSterilization.htmlCarl