I used to do this all the time. 1st edition and 2nd edition were so similar that I used any module any where, including what are now called BECMI modules. The stat block might be in different orders but it was all the same stuff. I knew the rules well enough and I ran it. To me it was all backwards compatible until 3rd edition came out.
2nd edition and BECMI both used THAC0. 1st Edition would say attacks as F1 or C2 or whatever. So there you go. F1 is Fighter 1 so THAC0=20, C2 is Cleric 2 so use that THAC0 and so on etc. Hit Points as in the stat block whichever system it came from. Saving Throws from 1ed was the same: Monster would save as F1, F2, F3 use that. I used 2nd Edition morale as it is faster to use.
You don't need every rule and you don't need all the stats. There really is not a need to convert much of anything from 1st to 2nd, or from BECMI for that matter. They were so similar... It was intuitive to me. You can also pick and choose rules from whichever Edition you like and and ignore the other two. If one does not make sense use the other, if one is too complicated use the other, and so on.