Yes, you can use the 64-bit kernel with 32-bit apps.
Does this work: LABEL tc
MENU LABEL Boot TinyCore
TEXT HELP
Boot TinyCore with Embedded X/GUI extensions.
Boot media is removable. Use TAB to edit options for specific needs.
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KERNEL /boot/vmlinuz64
INITRD /boot/rootfs.gz,/boot/modules64.gz
APPEND loglevel=3 cde