It's not icky. But it can be messy.

In my opinion, swiping-right would break the professional agreement you have and that breach of trust would carry over, outside. So, I think it's a bad option.

Slightly less provoking would be to say something but that doesn't seem to be a good option either for the same reasons.

On another note, take it from me, trying to cross that line will become more alluring/tempting as you begin to really trust and as the causes walls to break down. It can become an emotional roller coaster, like we all need more of. /s If you want the best healing you can get out of the experience, make some hard boundaries with yourself. (Remember, your emotional release, that you experience, will release-into your body, all the same chemicals it does when you are in love or lust.

If you stop seeing the person as a therapist, give it a break before you thing of asking them out.