ZKC Controller experienced a loss of separation with opposite direction traffic when accepting a misdirected hand off and trying to facilitate the correct procedure; noting future plans to refuse procedural errors.

Narrative

I was working Sector 62 RADAR combined with Sector 72 with a D-Side. Weather was impacting the sector with scattered cells to the south side and numerous deviations. Frequency congestion was also a factor. An E145 was handed to me north of my sector landing SGF out of FL300 descending at approximately 3000 FPM. This aircraft should have been handed off to Trails Sector 42 so I bought it and flashed to them to try and facilitate the hand-off. Sector 42 bought the hand-off but the E145 showed up on my frequency. I made sure 42 was watching; then descended the E145 to FL190 because of traffic; a BE58 in his face at FL180. Was to busy to watch it close enough to try to get the E145 under the BE58. Thought I heard the E145 say he saw the traffic passing off his right; in actuality he never said 'passing' just that he had him in sight well off the right. Thinking I was good; I descended the E145 and shipped him to Approach so they could continue his decent. Later I was informed it was a deal. I misapplied the rule. In hind sight; I will never again work an aircraft that should be worked by another controller.