There is no way.
This question is basically a duplicate of Is there a way to hide the new HTML5 spinbox controls shown in Google Chrome & Opera? but maybe not a full duplicate, since the motivation is given.
If the purpose is “browser's awareness of the content being purely numeric”, then you need to consider what that would really mean. The arrows, or spinners, are part of making numeric input more comfortable in some cases. Another part is checking that the content is a valid number, and on browsers that support HTML5 input enhancements, you might be able to do that using the pattern attribute. That attribute may also affect a third input feature, namely the type of virtual keyboard that may appear.
For example, if the input should be exactly five digits (like postal numbers might be, in some countries), then <input type="text" pattern="[0-9]{5}"> could be adequate. It is of course implementation-dependent how it will be handled.