In case you opt for filing of the Writ Petition then as per the High Court Rules it is the prerogative of the Chief Justice to appoint judge of his choice. Otherwise also the High Court has the power of supritendence and is very much within its right to call for the records of the lower court. My only anxiety is whether as per the rules whether you have sought (or have already got the NOC from the statutory authorities in this regard).
Last but not least the Writ is also suggested as thereafter you have an option to move to Apex Court in SLP. You may keep your options open.
In some states the judicial officers are entrusted with both civil and criminal matters and as such it is obvious that a CJM also handles civil matter. I have personal experience of noticing the same in Punjab as well.