There are a number of rhyming codes you can enter into the floor of Treasure Trove Cove's sandcastle that unlock the areas for those items, although I don't know what they are off the top of my head (and most gaming sites are blocked where I work).
Alternatively, you can play the Xbox Live Arcade release, which does implement Stop 'n Swop with Banjo-Tooie's XBLA release. The items are collectible after you defeat Gruntilda.
(Edit) You may need either a Banjo-Kazooie: Nuts & Bolts save or Banjo-Tooie on the same 360 to access the Stop 'n Swop items.
Side Note: Banjo-Tooie's XBLA release had a Stop 'n Swop II, the purpose of which isn't actually clear since it doesn't appear to integrate with Banjo-Kazooie: Nuts & Bolts.
(Edit) New Stop 'n Swop II items (eggs?) replaced the eggs and Ice Key in BT, which are now only available in BK.
And now, finally, here are the Treasure Trove Cove codes to open the secret items:
First, enter the code CHEAT.
To remove the ice wall in Freezyeasy Peak for the Ice Key, enter:
NOW YOU CAN SEE A NICE ICE KEY WHICH YOU CAN HAVE FOR FREE
To open the door in Gobi's Valley which has the Blue Egg behind it, enter:
A DESERT DOOR OPENS WIDE ANCIENT SECRETS WAIT INSIDE
To make Sharkfood Island rise in Treasure Trove Cove for the Purple Egg, enter:
OUT OF THE SEA IT RISES TO REVEAL MORE SECRET PRIZES
To open the X-marked Cask in the cellar of Mad Monster Mansion for the Cyan Egg, enter:
DONT YOU GO AND TELL HER ABOUT THE SECRET IN HER CELLAR
In Mad Monster Mansion, you can find the Green Egg in Loggo's bathroom if you enter:
AMIDST THE HAUNTED GLOOM A SECRET IN THE BATHROOM
Click Clock Wood has the Yellow Egg in Nabnut's house if you enter:
NOW BANJO WILL BE ABLE TO SEE IT ON NABNUTS TABLE
Rusty Bucket Bay is hiding the Red Egg in the Captain's Room if you enter:
THIS SECRET YOULL BE GRABBIN IN THE CAPTAINS CABIN
(Note that you have to enter said cabin from one of the windows, in case you've forgotten.)