Stephane Metral your questions has several components while the Title is given as . "Public Speaking training".

1. When you say corporation must keep up with productivity I understand that there is a Productivity issue. This can be dealt separately. I would like to focus on your CAPTION . about public speaking in this post.
2. "while facing continuous improvement through training & education" this is rather broad statement which encompasses . - Quality (continuous improvement . ISO 9001, TQM, etc. Not sure which for the organisation you have in mind) Training and Education is part related to A. Job Oriented Training and Education / Onboarding process or B, Post Appraisal Training . and Education which . covers the "Development Gap/s" that needs to be filled in the un-specified level of employees. I am skipping to elaborate on this as your CAPTION makes me believe that your . priority . is Public Speaking.
3. "what are the best strategies & available technological tools to train executives:" There are several Strategies and many Technological . tools available with different trainers after identification of . Training . NEEDS, future skilling and . Development needs. From . your . question I take it that it is Public . Speaking, Stage Fear, Specific occasion speaking as described below.
4. For e.g. keynote speakers - the focus group may be very small and may have the best of organisations' brains/ specialists/ subject matter specialists . with proven abilities and qualifications in their subject. There are several courses for them on Udemy.com by . T J Walker, Vanessa Van Edwards, Alexa Fischer, Jason Tedeak etc. and there are Executive Coaches available for a fee for One-on-One training to these C-Level Executives, Board . members, Functional Heads, Chairperson, Managing . Director etc. Age is no . barrier here. as even a successful . younger . Startup . may .evoke interest.
5. "and sales team " - Public speaking by Sales people to advanced public speaking in trade show, conference rooms, has . to do with . Sales Pitching which has to go thru the process and technique . training in sales comprising of Exploration, Need Identification, Features, Advantages, Benefits, Objection Handling, Negotiation, Closure in One on one and group . situations and there are many . sales training organisations in the world who provide Sales Effectiveness Coaching, Training for a fee.
6. "webinars" . are not restricted to Sales teams only - even Technical subjects with . a shorter ONLINE interactive talk with . content similar to Keynote address could be the . theme. There . are . Digital . marketing experts who impart this. I personally . recommend TOASTMASTERS and other social clubs who impart scientific Training and exposure as Physical clubs, Corporate Clubs and Online . Clubs with self assessment . tools and choice of 11 programs can help all levels of employees and Executives to go thru the training.
7. TED Talks again needs something EXTRAORDINARY, Contemporary . yet touching a social issue, invention, disruption etc and has a 17-18 minute speech decorum which can be viewed on their . websites and one can see thousands of Youtube speeches to self-learn at . our own pace. There are, of course, specific TED, TED-X trainers . and curators who help for a fee.
8. "Conventions" AND I would add . Panel . Chair, Panel discussion, into . this. Udemy and . Toastmasters are best IMHO as they helped me personally apart from many Online Audiobooks, personal coaching courses . by the likes of Tony Robbins et al who . for a fee can coach the needy.

I hope, I was able to satisfy your . query. Feel free to ask for more information/ clarification where required. I shall be happy . to answer.

The best advice I can offer is to retain Tim Pollard, Founder/Principal of Oratium.com, to deliver his amazingly impactful day-and-a-half speakers seminar to help all staff members in question with this key skill. Tim's well-developed and proven approach is both different from the generic speaker coaches/seminars to be found everywhere and has impacted senior business speakers worldwide for the past two decades. Delivered to a group, Tim's seminar can be cost-effective and still intimate enough to really engage each seminar attendee. I'm proof [positive and have sponsored several others to attend these events as well!