bearing sustainability in my head, I can recommend the swap to everybody trusting in his / her serious antistatic and technical skills and, of course, having around the pro-tech-tool-set from iFixit-
My wife loved working with her 2010 MBA 11" C2D-Board (2GB RAM, 128 GB SSD) with was in terms of productive work EOL. (The problem in Sierra and later, High Sierra was the poor 2GB RAM)
So, I got the following: MBA logic board i5 mid 2011 (4GB) AND a new battery. The board came with new cooling pipe and fan, which you will need. Take the time and get (f.e.) Arctic silver. Look for application-tutorials on youtube.
All connectors will fit, with the exception of the two (WIFI and BT2.1) – Cables going to the WIFI/BT-PCI-Board. You will have to extend them, soldering MHF4 MHF 4 right angle male plug 0.81mm Pigtail – Cable as extension. Take caution of very good shielding the soldering-points and carefully re-route the cables.
For the enhanced features of continuity, I put in a new WIFI/BT-Board: BCM943224PCIEBT2 607-8182. Along with continuity activation tool even this feature runs like a charm.
Also, the older SSD (Original Apple-SSD (Toshiba) works great. All-in-costs for me: 220 €. My wife loves her "new" Air.