I am not sure if one of those filters would be suitable for a betta or not, I only ever use box/corner filters because you can adjust the air flow. Bettas are not great swimmers and do not like a strong current. As for being noisy I am not sure but you will find that you get used to the noise, when I first started running filters in my room they woke me up a bit for the first couple of night but once I got used to them if we ever had a power cut and the filters went off I couldn't sleep because it was too silent!
Umm with the heater cord you could maybe get someone to melt/drill a hole for the lead to go through the cover? Also if you found the filter was too strong you could get a box/corner filter for the tank (they are really cheap) and run the airline tubing through the heater cord hole. Just an idea, let us know what you decide, if you do get it I would love to see some photos of when it is all set up!