Is it OK to simply dd the 128GB disk to the 32GB disk using count to stop after the 16GB partition was cloned?

I think it would work, but it seems a little overcomplicated, you can just use the partition paths as if and of of dd directly, as long as the output partition is not smaller than the input partition. For example dd if=/dev/sdc1 of=/dev/sdd1 bs=4M status=progress

Your method would also copy the partition table I suppose, which might be something you want under specific circumstances, but then it would be a little harder to get the count right, just taking the size of partition 1 would be wrong, because there is some space before it (where the partition table lives) and dd would start at 0. You'd need to add up the start position and the size of partition 1 instead.

Personally I would prefer making a new partition table on the new eMCC, and create a target partition on it. Then you clone the content of the partition (i.e. the file system). This way the file system UUID will still be the same, and the fstab should still work because these days it usually refers to mounts by filesystem UUID in my experience.

If you make the target partition larger than the source partition, and you intend to use the full partition going forward you will additionally need to resize the filesystem to fit the new larger partition, for example with resize2fs.