With a strapless monitor, it will probably have many other cycling specific functions, speed, time and distance etc.
With some strapless heart rate monitors this is possible with an attachment, but it will always look like a cycle computer on your wrist.
If you have the Shimano or Campagnolo cycle computer system on your handlebars, they tell you all your bike information and you would only want the basic heart rate read out as an extra, you wouldn’t need the same information twice, so a pulse rate monitor only would be best.
If you need more information in one unit then it is best to get a strapless heart rate monitor, Polar now do strapless monitors to add to there large wrist watch range, also available are CicloSport and CardioSport, and others, that also fit on the handlebars.