Subwoofer connection to integrated

i have an integrated tube amp that has no preouts, just 4 inputs. this is connected to some monitors that are rated down to 55hz. i am looking to buy a sub and going the speaker level input route seems the only way to go. i also want to cut the monitors off at 80hz and let the sub do the work. if i run speaker level from the integrated to the sub and then off the sub to my monitors{sub would have a 80hz high pass filter coming out}, would there be any issues doing it this way? are there any other options?
Nope, that's exactly how you should do it.

Look at subwoofers very carefully, as many do not have high pass filters. The crossover adjustment is for the low pass filer. The extra set of connectors are there for convenience only. Call the manufacturer's tech support when in doubt.
Me I personally crossover at 32hz when my speakers are rated to 45hz. I kick the volume up when doing that. With your eyes closed you can't point to the sub or speakers. For me if I crossover at or above the speaker rating I hear the subs location. Also I found the hardest part of setting up the sub is getting the phasing right. I have a Rel B3 and your only choice is 0 or 180 degrees. So you may have to re-position either the sub or speakers to get right on. Once that's done you will really appreciate how the sub helps with the mid range and sound stage let alone the low notes.
I would run a bi-wire configuration. One run to the montors and one run to the sub.
That way you don't have the low pass affecting your monitors.
I agree to run the monitors and sub separately, but the low pass will not affect the monitors the other way. The output speaker connectors on the sub will either be full range or a high pass filter, which is generally a fixed frequency, and not affected by the crossover adjustment.
i will definently experiment both ways but would like to have the option of the high pass filter.