Requires the custom walker class found in class-walker-taxonomy-radio-list.php.

taxonomy-meta-box-without-adder-with-radio-inputs.php

<?php
/**
 * Displays a custom taxonomy meta box with radio inputs.
 *
 * @param WP_Post $post Current post object.
 * @param array $box Categories meta box arguments.
 * @return void
 */
function toms_custom_meta_box_with_radio_inputs( WP_Post $post, array $box ): void {
	$tax_name = esc_attr( $box['args']['taxonomy'] );
	?>
	<div id="taxonomy-<?php echo $tax_name; ?>" class="categorydiv toms-custom-meta-box">
		<?php echo "<input type='hidden' name='tax_input[' . $tax_name . ']' value='0' />"; ?>
		<ul id="<?php echo $tax_name; ?>radiolist" data-wp-lists="list:<?php echo $tax_name; ?>" class="categorychecklist form-no-clear">
			<?php
			wp_terms_checklist(
				$post->ID,
				array(
					'taxonomy' => $tax_name,
					'walker'   => new Walker_Taxonomy_Radio_List(),
				)
			);
			?>
		</ul>
	</div>
	<?php
}

Requires the custom walker class found in https://gist.github.com/tomdevisser29/cd6f43f6111c3f1ec9aa4b3c319e0f17.