I'm not sure I'm following you 100%, but I'll give it a shot.
The work flow you're trying to use should be possible.
1. When you say that the "Get Data For ArcPad" buttons don't show up, is it that they're missing completely or are the icons grayed out?
The GPS Analyst toolbar v2.3 does not contain "Get Data For ArcPad" buttons like you would see on the ArcPad Data Manager toolbar. To check in and out you must utilize the two AXF buttons on the right side of the toolbar. When you hover over them they say "Get Data For ArcPad" and "Check in ArcPad AXF file and GPScorrect SSF". These are essentially the same tools as you would see on the ArcPad Data Manager toolbar, except the check in process checks in the SSF to the geodatabase as well.
The ArcPad toolbar (the short three-icon toolbar) was deprecated at version 10.
Because of this, in ArcMap 10 you can no longer check out to shapefile as you could at version 9.3.1. You must check the data out to axf for disconnected editing (which is the functionality that the ArcPad Data Manager toolbar utilizes).
2. If the buttons are grayed out, make sure that you've checked on both the ArcPad Data Manager and Trimble GPS Analyst extensions in the Customize Menu > Extensions list.
Hope this helps.