It's Christmas Eve, so there are no sane people around to answer your question... just me.

I believe that you have to run setup.exe to enter a new registration key. That does not mean you have to run a full setup. When you run a setup on top of an existing installation, you get more menu options, like "Add".

Just in case it helps, here is a doc I wrote for myself back in The Dark Days when I was uninstalling and installing Version 10 repeatedly (for some reason lost in time)...

In your case, you might have been able to start at Step 4:

-----------------------------------------------------------------
-- 1. Uninstall SA 10 Software

-- Run:     Control Panel - Add or Remove Programs
-- Remove:  SQL Anywhere 10 Software

-----------------------------------------------------------------
-- 2. OPTIONAL - Uninstall SA 10 Docs

-- This really isn't necessary if all you're doing is
-- reinstalling the software.

-- Run:     Control Panel - Add or Remove Programs
-- Remove:  SQL Anywhere 10 Documentation

-----------------------------------------------------------------
-- 3. Install SA 10.0.0 GA Software

-- You can copy-and-paste the whole key even though
-- the input field is formatted into sections.

-- Run Developer GA:  SQLAnywhere_1000_Windows.exe
--    Use this key:   xxx...

-----------------------------------------------------------------
-- 4. Enable Full Functionality

-- You can copy-and-paste the whole key even though
-- the input field is formatted into sections.

-- This will be very fast.

-- Run again:        SQLAnywhere_1000_Windows.exe
--    Select:        "Add"
--    Use this key:  xxx...
--    Seats:         n..

-----------------------------------------------------------------
HA key: xxx...

-----------------------------------------------------------------
-- 5. Upgrade Software to 10.0.1

-- Run upgrade:  SQLAnywhere10_Windows_Patch_10.0.1.exe

-----------------------------------------------------------------
-- 6. OPTIONAL - Install SA 10.0.1 Docs

-- This really isn't necessary if all you're doing is
-- reinstalling the software.

-- Run docs:    SQLAnywhere10_Documentation_10.0.1.exe
--    Uncheck:  English Printable Books (PDF)

-----------------------------------------------------------------
-- 7. Apply Software EBF

-- Run EBF:  sa_1001_win32_ebf_3579.exe

-- end -- 

Just to complete the picture:

Starting with SA 12, you can simply re-key the SQL Anywhere software by using the new DBLIC -k option, cf. this question.