You do not loose rewards by delegating a given stake key to another pool. This is because your active stake for epoch N+1 is determined by a snapshot at the beginning of epoch N.
The term “wallet” may be a little confusing here. If you look at ADALite you’ll notice that is uses the term “Account” for the first level in your address space hierarchy. Have a look at BIP44 to understand deterministic hierarchical wallets.
In any case, it is best to use a HW wallet that supports BIP44 (e.g. Ledger X). If you do, each account in can be staked to a different pool. Consolidating to accounts is a variation of unstaking an account. The process is …
- Move all but 2 ADA to another account in epoch N
- Wait for epoch N+2 to unstake your stake key
- Move those 2 ADA + 2 ADA deposit that other account
When you move your stake around, you may want to be familiar with the concept of “cost per block” and perhaps more importantly “effective cost per block”. The difference in reward can be significant i.e. >30% In short, I’d recommend to look for a pool with low “effective cost per block” that also does some good in the world.