Enforce cursor shape on tmux sessions running in remote SSH machine

[3N4N]

Because of an issue which causes block-shaped cursor in WT to clearly show the text under it, I use vintage cursor. It's not ideal, but it lets me work. The problem is, when I SSH into a remote machine and attach a tmux session that I launched from a Linux suckless terminal which uses block-shaped cursor, WT also switches to block-shaped cursor. If I create new tmux windows/panes, they show the vintage cursor.

Is there any way I can enforce the vintage cursor shape in existing tmux windows/panes from WT?

CC'ing @DHowett for better visibility. Hope that's okay.

[3N4N]

I can reset the cursor with \033[0 q. I knew about escape codes to change cursor shapes to bar, block, underscore, &c, but obviously none of those supports WT's vintage cursor shape. Cursor reset code is terminal emulator specific, thankfully. Now I need a way to reliably execute the cursor reset code on all tmux panes/windows. I know about tmux send-keys, but that doesn't take into account panes where a program is already running (e.g., vim), so it's not reliable.