Hi !
1. You do not need proxy-arp ( the neighboring router arps for the nect-hop address which is the outside interface address)
2 if always the initiating packet that triggers the flow is strictly inside to outside then use SOURCE-NAT with POOL
3. if you need outside to inside and/or inside to outside flow then use STATIC NAT
( Note: Static NAT is defined like destination nat independent of the direction of the first flow so you must define the static nat translating from 2.2.2.2 to the inbside address)
with best regards
alexander