In short as Victor mentioned, the rates for a pair of currency vary from Bank to Bank. Banks also give special rates if the amount to be converted is large. Unless you are receiving large amounts, hopping / shopping will not help.
If you are getting paid in USD, i.e. that is what is agreed between you and your client, then the client's bank would be doing the conversion. You are your Bank have no say in this.
If you have agreed to get paid in the local currency of your client, then depending on the currency it may still get converted by the sending Bank or in-between. Say for example you are to get paid in Indonesian Rupiah IDR, the client's Bank or its Correspondent would convert this into USD as IDR doesn’t get settled. If you are getting say GBP or EUR, then yes the conversion would typically be done by your bank.
However it typically takes 2-4 days SWIFT Wire transfers, i.e. from the time your client initiates the transfers to the time it reaches your Bank.
And no you can't go shopping after the Wire has arrived. If you want to do it before then unless the amounts involved are large, no Bank would commit a rate to you.